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

option (c) is correct.

Given expression
`(7^(-5))^3` is equal to
`((1)/(7))^(15)`

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)=((1)/(a) )^m` , we have,

`(7^(-5))^3=(((1)/(7))^5)^3`

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

`(((1)/(7))^5)^3=((1)/(7))^(5\cdot 3)=((1)/(7))^(15)`

Thus, option (c) is correct.

Given expression
`(7^(-5))^3` is equal to
`((1)/(7))^(15)`