Divide powers

{"questions":[{"content":"$$7^8:7^3$$[[fill_choice_big-1]]","widgets":{"fill_choice_big-1":{"type":"fill_choice_big","options":["$7^5$","$7^{24}$","$7^{\\frac{8}{3}}$","$7^{11}$"],"placeholder":0,"answer":0}},"step":1,"hints":["The bases are the same: $7$ and $7$. When dividing powers with the same bases, we leave the base the same and subtract the exponents.","$7^8:7^3=7^{8-3}=7^5$."]}]}

{"questions":[{"content":"$$2^9:2^4$$[[fill_choice_big-1]]","widgets":{"fill_choice_big-1":{"type":"fill_choice_big","options":["$2^5$","$2^{13}$","$2^{\\frac{9}{4}}$","$2^4$"],"placeholder":0,"answer":0}},"step":1,"hints":["The bases are the same: $2$ and $2$. When dividing powers with the same bases, we leave the base the same and subtract the exponents.","$2^9:2^4=2^{9-4}=2^5$."]},{"content":"$$3^7:3^2$$[[fill_choice_big-2]]","widgets":{"fill_choice_big-2":{"type":"fill_choice_big","options":["$3^5$","$3^9$","$3^{\\frac{7}{2}}$","$3^2$"],"placeholder":0,"answer":0}},"step":1,"hints":["The bases are the same: $3$ and $3$. When dividing powers with the same bases, we leave the base the same and subtract the exponents.","$3^7:3^2=3^{7-2}=3^5$."]},{"content":"$$5^{12}:5^7$$[[fill_choice_big-3]]","widgets":{"fill_choice_big-3":{"type":"fill_choice_big","options":["$5^5$","$5^{19}$","$5^{\\frac{12}{7}}$","$5^7$"],"placeholder":0,"answer":0}},"step":1,"hints":["The bases are the same: $5$ and $5$. When dividing powers with the same bases, we leave the base the same and subtract the exponents.","$5^{12}:5^7=5^{12-7}=5^5$."]},{"content":"$$7^{10}:7^6$$[[fill_choice_big-4]]","widgets":{"fill_choice_big-4":{"type":"fill_choice_big","options":["$7^4$","$7^{16}$","$7^{\\frac{10}{6}}$","$7^6$"],"placeholder":0,"answer":0}},"step":1,"hints":["The bases are the same: $7$ and $7$. When dividing powers with the same bases, we leave the base the same and subtract the exponents.","$7^{10}:7^6=7^{10-6}=7^4$."]},{"content":"$$4^8:4^3$$[[fill_choice_big-5]]","widgets":{"fill_choice_big-5":{"type":"fill_choice_big","options":["$4^5$","$4^{11}$","$4^{\\frac{8}{3}}$","$4^3$"],"placeholder":0,"answer":0}},"step":1,"hints":["The bases are the same: $4$ and $4$. When dividing powers with the same bases, we leave the base the same and subtract the exponents.","$4^8:4^3=4^{8-3}=4^5$."]},{"content":"$$6^{11}:6^5$$[[fill_choice_big-6]]","widgets":{"fill_choice_big-6":{"type":"fill_choice_big","options":["$6^6$","$6^{16}$","$6^{\\frac{11}{5}}$","$6^5$"],"placeholder":0,"answer":0}},"step":1,"hints":["The bases are the same: $6$ and $6$. When dividing powers with the same bases, we leave the base the same and subtract the exponents.","$6^{11}:6^5=6^{11-5}=6^6$."]},{"content":"$$9^6:9^1$$[[fill_choice_big-7]]","widgets":{"fill_choice_big-7":{"type":"fill_choice_big","options":["$9^5$","$9^6$","$9^{\\frac{6}{1}}$","$9^7$"],"placeholder":0,"answer":0}},"step":1,"hints":["The bases are the same: $9$ and $9$. When dividing powers with the same bases, we leave the base the same and subtract the exponents.","$9^6:9^1=9^{6-1}=9^5$."]},{"content":"$$8^7:8^4$$[[fill_choice_big-8]]","widgets":{"fill_choice_big-8":{"type":"fill_choice_big","options":["$8^3$","$8^{11}$","$8^{\\frac{7}{4}}$","$8^4$"],"placeholder":0,"answer":0}},"step":1,"hints":["The bases are the same: $8$ and $8$. When dividing powers with the same bases, we leave the base the same and subtract the exponents.","$8^7:8^4=8^{7-4}=8^3$."]},{"content":"$$10^9:10^2$$[[fill_choice_big-9]]","widgets":{"fill_choice_big-9":{"type":"fill_choice_big","options":["$10^7$","$10^{11}$","$10^{\\frac{9}{2}}$","$10^2$"],"placeholder":0,"answer":0}},"step":1,"hints":["The bases are the same: $10$ and $10$. When dividing powers with the same bases, we leave the base the same and subtract the exponents.","$10^9:10^2=10^{9-2}=10^7$."]},{"content":"$$11^5:11^3$$[[fill_choice_big-10]]","widgets":{"fill_choice_big-10":{"type":"fill_choice_big","options":["$11^2$","$11^8$","$11^{\\frac{5}{3}}$","$11^3$"],"placeholder":0,"answer":0}},"step":1,"hints":["The bases are the same: $11$ and $11$. When dividing powers with the same bases, we leave the base the same and subtract the exponents.","$11^5:11^3=11^{5-3}=11^2$."]},{"content":"$$12^4:12^2$$[[fill_choice_big-11]]","widgets":{"fill_choice_big-11":{"type":"fill_choice_big","options":["$12^2$","$12^6$","$12^{\\frac{4}{2}}$","$12^1$"],"placeholder":0,"answer":0}},"step":1,"hints":["The bases are the same: $12$ and $12$. When dividing powers with the same bases, we leave the base the same and subtract the exponents.","$12^4:12^2=12^{4-2}=12^2$."]},{"content":"$$13^9:13^8$$[[fill_choice_big-12]]","widgets":{"fill_choice_big-12":{"type":"fill_choice_big","options":["$13^1$","$13^{17}$","$13^{\\frac{9}{8}}$","$13^8$"],"placeholder":0,"answer":0}},"step":1,"hints":["The bases are the same: $13$ and $13$. When dividing powers with the same bases, we leave the base the same and subtract the exponents.","$13^9:13^8=13^{9-8}=13^1$."]},{"content":"$$14^7:14^5$$[[fill_choice_big-13]]","widgets":{"fill_choice_big-13":{"type":"fill_choice_big","options":["$14^2$","$14^{12}$","$14^{\\frac{7}{5}}$","$14^5$"],"placeholder":0,"answer":0}},"step":1,"hints":["The bases are the same: $14$ and $14$. When dividing powers with the same bases, we leave the base the same and subtract the exponents.","$14^7:14^5=14^{7-5}=14^2$."]},{"content":"$$15^6:15^4$$[[fill_choice_big-14]]","widgets":{"fill_choice_big-14":{"type":"fill_choice_big","options":["$15^2$","$15^{10}$","$15^{\\frac{6}{4}}$","$15^4$"],"placeholder":0,"answer":0}},"step":1,"hints":["The bases are the same: $15$ and $15$. When dividing powers with the same bases, we leave the base the same and subtract the exponents.","$15^6:15^4=15^{6-4}=15^2$."]},{"content":"$$16^{10}:16^7$$[[fill_choice_big-15]]","widgets":{"fill_choice_big-15":{"type":"fill_choice_big","options":["$16^3$","$16^{17}$","$16^{\\frac{10}{7}}$","$16^7$"],"placeholder":0,"answer":0}},"step":1,"hints":["The bases are the same: $16$ and $16$. When dividing powers with the same bases, we leave the base the same and subtract the exponents.","$16^{10}:16^7=16^{10-7}=16^3$."]},{"content":"$$18^5:18^1$$[[fill_choice_big-16]]","widgets":{"fill_choice_big-16":{"type":"fill_choice_big","options":["$18^4$","$18^6$","$18^{\\frac{5}{1}}$","$18^5$"],"placeholder":0,"answer":0}},"step":1,"hints":["The bases are the same: $18$ and $18$. When dividing powers with the same bases, we leave the base the same and subtract the exponents.","$18^5:18^1=18^{5-1}=18^4$."]},{"content":"$$19^8:19^3$$[[fill_choice_big-17]]","widgets":{"fill_choice_big-17":{"type":"fill_choice_big","options":["$19^5$","$19^{11}$","$19^{\\frac{8}{3}}$","$19^3$"],"placeholder":0,"answer":0}},"step":1,"hints":["The bases are the same: $19$ and $19$. When dividing powers with the same bases, we leave the base the same and subtract the exponents.","$19^8:19^3=19^{8-3}=19^5$."]},{"content":"$$20^6:20^2$$[[fill_choice_big-18]]","widgets":{"fill_choice_big-18":{"type":"fill_choice_big","options":["$20^4$","$20^8$","$20^{\\frac{6}{2}}$","$20^2$"],"placeholder":0,"answer":0}},"step":1,"hints":["The bases are the same: $20$ and $20$. When dividing powers with the same bases, we leave the base the same and subtract the exponents.","$20^6:20^2=20^{6-2}=20^4$."]},{"content":"$$21^{9}:21^4$$[[fill_choice_big-19]]","widgets":{"fill_choice_big-19":{"type":"fill_choice_big","options":["$21^5$","$21^{13}$","$21^{\\frac{9}{4}}$","$21^4$"],"placeholder":0,"answer":0}},"step":1,"hints":["The bases are the same: $21$ and $21$. When dividing powers with the same bases, we leave the base the same and subtract the exponents.","$21^9:21^4=21^{9-4}=21^5$."]},{"content":"$$24^7:24^6$$[[fill_choice_big-20]]","widgets":{"fill_choice_big-20":{"type":"fill_choice_big","options":["$24^1$","$24^{13}$","$24^{\\frac{7}{6}}$","$24^6$"],"placeholder":0,"answer":0}},"step":1,"hints":["The bases are the same: $24$ and $24$. When dividing powers with the same bases, we leave the base the same and subtract the exponents.","$24^7:24^6=24^{7-6}=24^1$."]}]}

{"questions":[{"content":"$$2^6:4^6$$[[fill_choice_big-1]]","widgets":{"fill_choice_big-1":{"type":"fill_choice_big","options":["$\\left(\\frac{1}{2}\\right)^6$","$2^{12}$","$\\left(\\frac{2}{4}\\right)^{12}$","$\\left(\\frac{1}{2}\\right)^{12}$"],"placeholder":0,"answer":0}},"step":1,"hints":["The exponents are the same: $6$ and $6$. When dividing powers with the same exponents, use the $a^n:b^n=\\left(\\frac{a}{b}\\right)^n$ rule.","$2^6:4^6=\\left(\\frac{2}{4}\\right)^6=\\left(\\frac{1}{2}\\right)^6$."]},{"content":"$$3^5:6^5$$[[fill_choice_big-2]]","widgets":{"fill_choice_big-2":{"type":"fill_choice_big","options":["$\\left(\\frac{1}{2}\\right)^5$","$\\left(\\frac{2}{1}\\right)^5$","$\\left(\\frac{3}{6}\\right)^{10}$","$\\left(\\frac{1}{3}\\right)^5$"],"placeholder":0,"answer":0}},"step":1,"hints":["The exponents are the same: $5$ and $5$. When dividing powers with the same exponents, use the $a^n:b^n=\\left(\\frac{a}{b}\\right)^n$ rule.","$3^5:6^5=\\left(\\frac{3}{6}\\right)^5=\\left(\\frac{1}{2}\\right)^5$."]},{"content":"$$5^4:10^4$$[[fill_choice_big-3]]","widgets":{"fill_choice_big-3":{"type":"fill_choice_big","options":["$\\left(\\frac{1}{2}\\right)^4$","$2^4$","$\\left(\\frac{5}{10}\\right)^8$","$\\left(\\frac{1}{5}\\right)^4$"],"placeholder":0,"answer":0}},"step":1,"hints":["The exponents are the same: $4$ and $4$. When dividing powers with the same exponents, use the $a^n:b^n=\\left(\\frac{a}{b}\\right)^n$ rule.","$5^4:10^4=\\left(\\frac{5}{10}\\right)^4=\\left(\\frac{1}{2}\\right)^4$."]},{"content":"$$7^3:14^3$$[[fill_choice_big-4]]","widgets":{"fill_choice_big-4":{"type":"fill_choice_big","options":["$\\left(\\frac{1}{2}\\right)^3$","$\\left(\\frac{2}{1}\\right)^3$","$\\left(\\frac{7}{14}\\right)^6$","$\\left(\\frac{1}{7}\\right)^3$"],"placeholder":0,"answer":0}},"step":1,"hints":["The exponents are the same: $3$ and $3$. When dividing powers with the same exponents, use the $a^n:b^n=\\left(\\frac{a}{b}\\right)^n$ rule.","$7^3:14^3=\\left(\\frac{7}{14}\\right)^3=\\left(\\frac{1}{2}\\right)^3$."]},{"content":"$$8^2:4^2$$[[fill_choice_big-5]]","widgets":{"fill_choice_big-5":{"type":"fill_choice_big","options":["$2^2$","$\\left(\\frac{1}{2}\\right)^2$","$\\left(\\frac{8}{4}\\right)^4$","$4^2$"],"placeholder":0,"answer":0}},"step":1,"hints":["The exponents are the same: $2$ and $2$. When dividing powers with the same exponents, use the $a^n:b^n=\\left(\\frac{a}{b}\\right)^n$ rule.","$8^2:4^2=\\left(\\frac{8}{4}\\right)^2=2^2$."]},{"content":"$$9^3:3^3$$[[fill_choice_big-6]]","widgets":{"fill_choice_big-6":{"type":"fill_choice_big","options":["$3^3$","$\\left(\\frac{1}{3}\\right)^3$","$\\left(\\frac{9}{3}\\right)^6$","$9^0$"],"placeholder":0,"answer":0}},"step":1,"hints":["The exponents are the same: $3$ and $3$. When dividing powers with the same exponents, use the $a^n:b^n=\\left(\\frac{a}{b}\\right)^n$ rule.","$9^3:3^3=\\left(\\frac{9}{3}\\right)^3=3^3$."]},{"content":"$$12^4:3^4$$[[fill_choice_big-7]]","widgets":{"fill_choice_big-7":{"type":"fill_choice_big","options":["$4^4$","$\\left(\\frac{1}{4}\\right)^4$","$12^{16}$","$\\left(\\frac{12}{3}\\right)^8$"],"placeholder":0,"answer":0}},"step":1,"hints":["The exponents are the same: $4$ and $4$. When dividing powers with the same exponents, use the $a^n:b^n=\\left(\\frac{a}{b}\\right)^n$ rule.","$12^4:3^4=\\left(\\frac{12}{3}\\right)^4=4^4$."]},{"content":"$$15^2:5^2$$[[fill_choice_big-8]]","widgets":{"fill_choice_big-8":{"type":"fill_choice_big","options":["$3^2$","$\\left(\\frac{1}{3}\\right)^2$","$\\left(\\frac{15}{5}\\right)^4$","$5^2$"],"placeholder":0,"answer":0}},"step":1,"hints":["The exponents are the same: $2$ and $2$. When dividing powers with the same exponents, use the $a^n:b^n=\\left(\\frac{a}{b}\\right)^n$ rule.","$15^2:5^2=\\left(\\frac{15}{5}\\right)^2=3^2$."]},{"content":"$$16^3:8^3$$[[fill_choice_big-9]]","widgets":{"fill_choice_big-9":{"type":"fill_choice_big","options":["$2^3$","$\\left(\\frac{1}{2}\\right)^3$","$\\left(\\frac{16}{8}\\right)^6$","$8^3$"],"placeholder":0,"answer":0}},"step":1,"hints":["The exponents are the same: $3$ and $3$. When dividing powers with the same exponents, use the $a^n:b^n=\\left(\\frac{a}{b}\\right)^n$ rule.","$16^3:8^3=\\left(\\frac{16}{8}\\right)^3=2^3$."]},{"content":"$$18^2:6^2$$[[fill_choice_big-10]]","widgets":{"fill_choice_big-10":{"type":"fill_choice_big","options":["$3^2$","$\\left(\\frac{1}{3}\\right)^2$","$\\left(\\frac{18}{6}\\right)^4$","$6^0$"],"placeholder":0,"answer":0}},"step":1,"hints":["The exponents are the same: $2$ and $2$. When dividing powers with the same exponents, use the $a^n:b^n=\\left(\\frac{a}{b}\\right)^n$ rule.","$18^2:6^2=\\left(\\frac{18}{6}\\right)^2=3^2$."]},{"content":"$$20^3:5^3$$[[fill_choice_big-11]]","widgets":{"fill_choice_big-11":{"type":"fill_choice_big","options":["$4^3$","$\\left(\\frac{1}{4}\\right)^3$","$\\left(\\frac{20}{5}\\right)^6$","$5^3$"],"placeholder":0,"answer":0}},"step":1,"hints":["The exponents are the same: $3$ and $3$. When dividing powers with the same exponents, use the $a^n:b^n=\\left(\\frac{a}{b}\\right)^n$ rule.","$20^3:5^3=\\left(\\frac{20}{5}\\right)^3=4^3$."]},{"content":"$$24^2:6^2$$[[fill_choice_big-12]]","widgets":{"fill_choice_big-12":{"type":"fill_choice_big","options":["$4^2$","$\\left(\\frac{1}{4}\\right)^2$","$\\left(\\frac{24}{6}\\right)^4$","$6^2$"],"placeholder":0,"answer":0}},"step":1,"hints":["The exponents are the same: $2$ and $2$. When dividing powers with the same exponents, use the $a^n:b^n=\\left(\\frac{a}{b}\\right)^n$ rule.","$24^2:6^2=\\left(\\frac{24}{6}\\right)^2=4^2$."]},{"content":"$$25^3:5^3$$[[fill_choice_big-13]]","widgets":{"fill_choice_big-13":{"type":"fill_choice_big","options":["$5^3$","$\\left(\\frac{1}{5}\\right)^3$","$\\left(\\frac{25}{5}\\right)^6$","$25^0$"],"placeholder":0,"answer":0}},"step":1,"hints":["The exponents are the same: $3$ and $3$. When dividing powers with the same exponents, use the $a^n:b^n=\\left(\\frac{a}{b}\\right)^n$ rule.","$25^3:5^3=\\left(\\frac{25}{5}\\right)^3=5^3$."]},{"content":"$$27^2:9^2$$[[fill_choice_big-14]]","widgets":{"fill_choice_big-14":{"type":"fill_choice_big","options":["$3^2$","$\\left(\\frac{1}{3}\\right)^2$","$\\left(\\frac{27}{9}\\right)^4$","$9^2$"],"placeholder":0,"answer":0}},"step":1,"hints":["The exponents are the same: $2$ and $2$. When dividing powers with the same exponents, use the $a^n:b^n=\\left(\\frac{a}{b}\\right)^n$ rule.","$27^2:9^2=\\left(\\frac{27}{9}\\right)^2=3^2$."]},{"content":"$$28^3:7^3$$[[fill_choice_big-15]]","widgets":{"fill_choice_big-15":{"type":"fill_choice_big","options":["$4^3$","$\\left(\\frac{1}{4}\\right)^3$","$\\left(\\frac{28}{7}\\right)^6$","$7^3$"],"placeholder":0,"answer":0}},"step":1,"hints":["The exponents are the same: $3$ and $3$. When dividing powers with the same exponents, use the $a^n:b^n=\\left(\\frac{a}{b}\\right)^n$ rule.","$28^3:7^3=\\left(\\frac{28}{7}\\right)^3=4^3$."]},{"content":"$$30^2:15^2$$[[fill_choice_big-16]]","widgets":{"fill_choice_big-16":{"type":"fill_choice_big","options":["$2^2$","$\\left(\\frac{1}{2}\\right)^2$","$\\left(\\frac{30}{15}\\right)^4$","$15^2$"],"placeholder":0,"answer":0}},"step":1,"hints":["The exponents are the same: $2$ and $2$. When dividing powers with the same exponents, use the $a^n:b^n=\\left(\\frac{a}{b}\\right)^n$ rule.","$30^2:15^2=\\left(\\frac{30}{15}\\right)^2=2^2$."]},{"content":"$$32^4:16^4$$[[fill_choice_big-17]]","widgets":{"fill_choice_big-17":{"type":"fill_choice_big","options":["$2^4$","$\\left(\\frac{1}{2}\\right)^4$","$\\left(\\frac{32}{16}\\right)^8$","$16^4$"],"placeholder":0,"answer":0}},"step":1,"hints":["The exponents are the same: $4$ and $4$. When dividing powers with the same exponents, use the $a^n:b^n=\\left(\\frac{a}{b}\\right)^n$ rule.","$32^4:16^4=\\left(\\frac{32}{16}\\right)^4=2^4$."]},{"content":"$$36^2:6^2$$[[fill_choice_big-18]]","widgets":{"fill_choice_big-18":{"type":"fill_choice_big","options":["$6^2$","$\\left(\\frac{1}{6}\\right)^2$","$\\left(\\frac{36}{6}\\right)^4$","$6^0$"],"placeholder":0,"answer":0}},"step":1,"hints":["The exponents are the same: $2$ and $2$. When dividing powers with the same exponents, use the $a^n:b^n=\\left(\\frac{a}{b}\\right)^n$ rule.","$36^2:6^2=\\left(\\frac{36}{6}\\right)^2=6^2$."]},{"content":"$$45^3:15^3$$[[fill_choice_big-19]]","widgets":{"fill_choice_big-19":{"type":"fill_choice_big","options":["$3^3$","$\\left(\\frac{1}{3}\\right)^3$","$\\left(\\frac{45}{15}\\right)^6$","$15^3$"],"placeholder":0,"answer":0}},"step":1,"hints":["The exponents are the same: $3$ and $3$. When dividing powers with the same exponents, use the $a^n:b^n=\\left(\\frac{a}{b}\\right)^n$ rule.","$45^3:15^3=\\left(\\frac{45}{15}\\right)^3=3^3$."]},{"content":"$$49^2:7^2$$[[fill_choice_big-20]]","widgets":{"fill_choice_big-20":{"type":"fill_choice_big","options":["$7^2$","$\\left(\\frac{1}{7}\\right)^2$","$\\left(\\frac{49}{7}\\right)^4$","$49^0$"],"placeholder":0,"answer":0}},"step":1,"hints":["The exponents are the same: $2$ and $2$. When dividing powers with the same exponents, use the $a^n:b^n=\\left(\\frac{a}{b}\\right)^n$ rule.","$49^2:7^2=\\left(\\frac{49}{7}\\right)^2=7^2$."]}]}