Question

Simplify the expression so there is only one positive power for each base. ​

Answer 1

Option (A)

Explanation:

The given expression is,

`(5^(-2)* 4^(-4))^(-2)`

Since
`x^(-1)=(1)/(x)` and
`(1)/(x^(-1))=x`

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

`4^(2)=(1)/(4^(-2))`

Therefore,
`(5^(-2)* 4^(-4))^(-2)=(1)/((5^(-2)* 4^(-4))^(2))`

`=(1)/((5^(-2))^2* (4^(-4))^2)`

`=(1)/(5^(-4)* 4^(-8))`

`=(1)/(5^(-4))* (1)/(4^(-8))`

`=5^(4)* 4^(8)`

Option (A) will be the answer.