Question

which of the following is equal to the expression below ? (7^-5 ) 3
a. (-1/7 ) -15
b. (1/7 ) ^-15
c. (1/7) ^15
d.(-1/7 ) ^15

Answer 1

Answer:

option (c) is correct.

Given expression $(7^{-5})^3$ is equal to  $(\frac{1}{7})^{15}$

Step-by-step explanation:

Given expression $(7^{-5})^3$

We have to choose a correct option from the given option that is equal to the given expression.

Consider the given expression $(7^{-5})^3$

Using property of exponents $a^{-m}=(\frac{1}{a} )^m$ , we have,

$(7^{-5})^3=((\frac{1}{7})^5)^3$

Again using property of exponents $(a^m)^n=a^{m\cdot n}$ , we have,

$((\frac{1}{7})^5)^3=(\frac{1}{7})^{5\cdot 3}=(\frac{1}{7})^{15}$

Thus, option (c) is correct.

Given expression $(7^{-5})^3$ is equal to  $(\frac{1}{7})^{15}$