Hello!
[tex]\large\boxed{\text{n = 5, m = 9, x = 512}}[/tex]
An exponential expression in form [tex]\sqrt[z]{x^{y} }[/tex] can be rewritten as [tex]x^{\frac{y}{z} }[/tex] where "z" is the root and "y" is the power. For example:
[tex]x^{\frac{2}{3} } = \sqrt[3]{x^{2} }[/tex].
We can apply this idea to this problem:
[tex](32)^{\frac{9}{5} } = (\sqrt[5]{32^{9} } )[/tex]
Therefore:
n = 5
m = 9
Simplify the expression:
[tex]\sqrt[5]{32^{9} } = (\sqrt[5]{32} )^{9}[/tex]
[tex]\sqrt[5]{32} = 2\\\\2^{9} = 512[/tex]
Therefore, the values of all letters are:
n = 5
m = 9
x = 512
