Question

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

Answer 1

ANSWER

$\frac{25}{16}$

EXPLANATION

We have the fraction:

$(\frac{4}{5})^{-2}$

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:

$(\frac{4}{5})^{-2}\text{ becomes (}\frac{5}{4})^2$

Simplifying that we have:

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

That is the answer.