Question

simplify (576/625)^power -1/2

Answer 1

Please refer to the attachment

Answer 2

Concept

A completely simplified fraction, that is, a fraction reduced to the lowest term, is a fraction that can no longer be simplified, the simplest equivalent fraction, the fraction with the smallest numerator and denominator possible, that is, prime numbers to each other. It has been reduced.

Given

We have given an expression which is $(\frac{576}{625} )^\frac{-1}{2}$ .

Find

We are asked to determine the value of the given expression.

Solution

Prime factorization of numerator is given by

$576=2^6\times3^2$

Prime factorization of denominator is given by

$625=5^4$

Putting this value in given expression, we get

$(\frac{576}{625} )^\frac{-1}{2}=(\frac{2^6\times3^2}{5^4} )^\frac{-1}{2}$

We will apply following identity  $(a^m)^n=a^m^n$ .On applying, we get  

    $\frac{2^-^3\times 3^-^1}{5^-^2}$

On simplifying , we get  $\frac{5^2}{2^3\times3}=\frac{25}{8\times3\\}=\frac{25}{24}$

Therefore, 25/24 is the answer of the given expression.

#SPJ2