Question

Enter the value of n = Enter the value of m = Enter the value of x =

Answer 1

Hello!

$\large\boxed{\text{n = 5, m = 9, x = 512}}$

An exponential expression in form $\sqrt[z]{x^{y} }$ can be rewritten as $x^{\frac{y}{z} }$ where "z" is the root and "y" is the power. For example:

$x^{\frac{2}{3} } = \sqrt[3]{x^{2} }$.

We can apply this idea to this problem:

$(32)^{\frac{9}{5} } = (\sqrt[5]{32^{9} } )$

Therefore:

n = 5

m = 9

Simplify the expression:

$\sqrt[5]{32^{9} } = (\sqrt[5]{32} )^{9}$

$\sqrt[5]{32} = 2\\\\2^{9} = 512$

Therefore, the values of all letters are:

n = 5

m = 9

x = 512