Question

(4/5)^(- 2)I need to rewrite this without an exponent.

Answer 1

`(25)/(16)`

Step-by-step explanation

We have the fraction:

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

To simplify this, we can apply a law of indices.

One of laws of indices states that if a fraction is raised to a negative power, we can simplify it by swapping the numerator and denominator and making the power positive.

In other words:

`((4)/(5))^(-2)\text{ becomes (}(5)/(4))^2`

Simplifying that we have:

`\begin{gathered} ((5)/(4))^2\text{ = }(5^2)/(4^2) \\ =\text{ }(25)/(16) \end{gathered}`

That is the answer.