Question

Which expression is equivalent to 5^4 × (5^-3)^2?

Answer 1

5^-2 or 1/25

Explanation:

use index laws.

1. (A^m)^n = a^mn

5^4 x (5^-3)^2=
5^4 x 5^-6

2. A^m x A^n = A^m+n

5^4 x 5^-6

5^-2=
1/5²=
1/25

Answer 2

`5^(4)* \left( 5^(-3)\right)^(2) =5^(-2)`

Explanation:

`5^(4)* \left( 5^(-3)\right)^(2) =5^(4)* 5^(-6)=5^(4-6)=5^(-2)`

We can write:

`5^(-2)=(1)/(5^(2)) =(1)/(25)`