Powers of a Fraction: System of equations with no solution

Combination of different basesComplete the equationPresenting powers in the denominator as powers with negative exponentsUsing multiple rulesApplying the formulaVariable in the exponent of the powerVariable in the base of the powerInverse formulaNumber of termsconverting Negative Exponents to Positive ExponentsCalculating powers with negative exponents
Question 1

\( \)Insert the corresponding expression:

\( \left(\frac{1}{2}\right)^2= \)

Question 2

Insert the corresponding expression:

\( \left(\frac{13}{19}\right)^7= \)

Question 3

Insert the corresponding expression:

\( \left(\frac{9}{20}\right)^6= \)

Question 4

Insert the corresponding expression:

\( \left(\frac{5}{6}\right)^{10}= \)

Question 5

Insert the corresponding expression:

\( \left(\frac{10}{13}\right)^8= \)

Examples with solutions for Powers of a Fraction: System of equations with no solution

Exercise #1

Insert the corresponding expression:

(12)2= \left(\frac{1}{2}\right)^2=

Video Solution

Answer

1222 \frac{1^2}{2^2}

Exercise #2

Insert the corresponding expression:

(1319)7= \left(\frac{13}{19}\right)^7=

Video Solution

Answer

137197 \frac{13^7}{19^7}

Exercise #3

Insert the corresponding expression:

(920)6= \left(\frac{9}{20}\right)^6=

Video Solution

Answer

96206 \frac{9^6}{20^6}

Exercise #4

Insert the corresponding expression:

(56)10= \left(\frac{5}{6}\right)^{10}=

Video Solution

Answer

510610 \frac{5^{10}}{6^{10}}

Exercise #5

Insert the corresponding expression:

(1013)8= \left(\frac{10}{13}\right)^8=

Video Solution

Answer

108138 \frac{10^8}{13^8}

Question 1

Insert the corresponding expression:

\( \left(\frac{5}{8}\right)^9= \)

Question 2

Insert the corresponding expression:

\( \left(\frac{2}{9}\right)^7= \)

Question 3

Insert the corresponding expression:

\( \left(\frac{3}{7}\right)^6= \)

Question 4

Insert the corresponding expression:

\( \left(\frac{20}{21}\right)^4= \)

Question 5

Insert the corresponding expression:

\( \left(\frac{4}{7}\right)^3= \)

Exercise #6

Insert the corresponding expression:

(58)9= \left(\frac{5}{8}\right)^9=

Video Solution

Answer

5989 \frac{5^9}{8^9}

Exercise #7

Insert the corresponding expression:

(29)7= \left(\frac{2}{9}\right)^7=

Video Solution

Answer

2797 \frac{2^7}{9^7}

Exercise #8

Insert the corresponding expression:

(37)6= \left(\frac{3}{7}\right)^6=

Video Solution

Answer

3676 \frac{3^6}{7^6}

Exercise #9

Insert the corresponding expression:

(2021)4= \left(\frac{20}{21}\right)^4=

Video Solution

Answer

204214 \frac{20^4}{21^4}

Exercise #10

Insert the corresponding expression:

(47)3= \left(\frac{4}{7}\right)^3=

Video Solution

Answer

4373 \frac{4^3}{7^3}

Question 1

Insert the corresponding expression:

\( \left(\frac{2}{3}\right)^2= \)

Question 2

Insert the corresponding expression:

\( \left(\frac{1}{5}\right)^3= \)

Question 3

Insert the corresponding expression:

\( \left(\frac{3}{8\times10}\right)^5= \)

Question 4

Insert the corresponding expression:

\( \)\( \left(\frac{4}{5\times7}\right)^4= \)

Question 5

Insert the corresponding expression:

\( \)\( \left(\frac{4}{2\times3}\right)^3= \)

Exercise #11

Insert the corresponding expression:

(23)2= \left(\frac{2}{3}\right)^2=

Video Solution

Answer

2232 \frac{2^2}{3^2}

Exercise #12

Insert the corresponding expression:

(15)3= \left(\frac{1}{5}\right)^3=

Video Solution

Answer

1353 \frac{1^3}{5^3}

Exercise #13

Insert the corresponding expression:

(38×10)5= \left(\frac{3}{8\times10}\right)^5=

Video Solution

Answer

a'+b' are correct

Exercise #14

Insert the corresponding expression:

(45×7)4= \left(\frac{4}{5\times7}\right)^4=

Video Solution

Answer

44(5×7)4 \frac{4^4}{\left(5\times7\right)^4}

Exercise #15

Insert the corresponding expression:

(42×3)3= \left(\frac{4}{2\times3}\right)^3=

Video Solution

Answer

43(2×3)3 \frac{4^3}{\left(2\times3\right)^3}

Question 1

Insert the corresponding expression:

\( \)\( \left(\frac{13\times21}{11\times10}\right)^6= \)

Question 2

Insert the corresponding expression:

\( \)\( \left(\frac{2\times3}{7\times9}\right)^7= \)

Question 3

Insert the corresponding expression:

\( \left(\frac{5\times9}{8\times10}\right)^3= \)

Question 4

Insert the corresponding expression:

\( \left(\frac{2\times6}{5\times7}\right)^4= \)

Question 5

Insert the corresponding expression:

\( \)\( \left(\frac{5\times7}{71}\right)^4= \)

Exercise #16

Insert the corresponding expression:

(13×2111×10)6= \left(\frac{13\times21}{11\times10}\right)^6=

Video Solution

Answer

136×216116×106 \frac{13^6\times21^6}{11^6\times10^6}

Exercise #17

Insert the corresponding expression:

(2×37×9)7= \left(\frac{2\times3}{7\times9}\right)^7=

Video Solution

Answer

27×3777×97 \frac{2^7\times3^7}{7^7\times9^7}

Exercise #18

Insert the corresponding expression:

(5×98×10)3= \left(\frac{5\times9}{8\times10}\right)^3=

Video Solution

Answer

53×9283×103 \frac{5^3\times9^2}{8^3\times10^3}

Exercise #19

Insert the corresponding expression:

(2×65×7)4= \left(\frac{2\times6}{5\times7}\right)^4=

Video Solution

Answer

All answers are correct

Exercise #20

Insert the corresponding expression:

(5×771)4= \left(\frac{5\times7}{71}\right)^4=

Video Solution

Answer

(5×7)4714 \frac{\left(5\times7\right)^4}{71^4}