Examples with solutions for Powers of a Fraction: Inverse formula

Exercise #1

Insert the corresponding expression:

3686= \frac{3^6}{8^6}=

Video Solution

Answer

(38)6 \left(\frac{3}{8}\right)^6

Exercise #2

Insert the corresponding expression:

29119= \frac{2^9}{11^9}=

Video Solution

Answer

(211)9 \left(\frac{2}{11}\right)^9

Exercise #3

Insert the corresponding expression:

1797= \frac{1^7}{9^7}=

Video Solution

Answer

(19)7 \left(\frac{1}{9}\right)^7

Exercise #4

Insert the corresponding expression:

2474= \frac{2^4}{7^4}=

Video Solution

Answer

(27)4 \left(\frac{2}{7}\right)^4

Exercise #5

Insert the corresponding expression:

1232= \frac{1^2}{3^2}=

Video Solution

Answer

(13)2 \left(\frac{1}{3}\right)^2

Exercise #6

Insert the corresponding expression:

710910= \frac{7^{10}}{9^{10}}=

Video Solution

Answer

(79)10 \left(\frac{7}{9}\right)^{10}

Exercise #7

Insert the corresponding expression:

204314= \frac{20^4}{31^4}=

Video Solution

Answer

(2031)4 \left(\frac{20}{31}\right)^4

Exercise #8

Insert the corresponding expression:

123233= \frac{12^3}{23^3}=

Video Solution

Answer

(1223)3 \left(\frac{12}{23}\right)^3

Exercise #9

Insert the corresponding expression:

1565= \frac{1^5}{6^5}=

Video Solution

Answer

(16)5 \left(\frac{1}{6}\right)^5

Exercise #10

Insert the corresponding expression:

105175= \frac{10^5}{17^5}=

Video Solution

Answer

(1017)5 \left(\frac{10}{17}\right)^5

Exercise #11

Insert the corresponding expression:

57×47197= \frac{5^7\times4^7}{19^7}=

Video Solution

Answer

A+B are correct

Exercise #12

Insert the corresponding expression:

65135×45= \frac{6^5}{13^5\times4^5}=

Video Solution

Answer

(613×4)5 \left(\frac{6}{13\times4}\right)^5

Exercise #13

Insert the corresponding expression:

4353×73= \frac{4^3}{5^3\times7^3}=

Video Solution

Answer

(45×7)3 \left(\frac{4}{5\times7}\right)^3

Exercise #14

Insert the corresponding expression:

66×11656×136= \frac{6^6\times11^6}{5^6\times13^6}=

Video Solution

Answer

A+B are correct

Exercise #15

Insert the corresponding expression:

510×810410×710= \frac{5^{10}\times8^{10}}{4^{10}\times7^{10}}=

Video Solution

Answer

(5×8)10(4×7)10 \frac{\left(5\times8\right)^{10}}{\left(4\times7\right)^{10}}

Exercise #16

Insert the corresponding expression:

29×39119×79= \frac{2^9\times3^9}{11^9\times7^9}=

Video Solution

Answer

a'+b' are correct

Exercise #17

Insert the corresponding expression:

68×78178= \frac{6^8\times7^8}{17^8}=

Video Solution

Answer

(6×7)8178 \frac{\left(6\times7\right)^8}{17^8}

Exercise #18

Insert the corresponding expression:

167= \frac{1}{6^7}=

Video Solution

Answer

67 6^{-7}

Exercise #19

Insert the corresponding expression:

132= \frac{1}{3^2}=

Video Solution

Answer

32 3^{-2}

Exercise #20

Insert the corresponding expression:

152= \frac{1}{5^2}=

Video Solution

Answer

52 5^{-2}