Answer :
Given the following expression:
[tex]\text{ 5}^{3.2^{}}\text{ = y}[/tex]To expand the given exponential expression, we first convert 5.2 into an improper fraction.
We get,
[tex]3.2\text{ = 3}\frac{20}{100}\text{ = 3}\frac{1}{5}[/tex][tex]\text{ 3}\frac{1}{5}\text{ = }\frac{1\text{ + (3 x 5)}}{5}\text{ = }\frac{1\text{ + 15}}{5}[/tex][tex]\text{ = }\frac{16}{5}[/tex]Reconstructing the expression, we get:
[tex]\text{ 5}^{3.2}\text{ = y }\rightarrow5^{\frac{16}{5}}=\text{ y}[/tex]When the exponent is a fraction, the numerator remains the exponent of the base while the denominator becomes the degree of the root.
We get,
[tex]\text{ 5}^{\frac{16}{5}}\text{ = y }\rightarrow\text{ }\sqrt[5]{5^{16}}\text{ = y}[/tex][tex]undefined[/tex]