Question

The number forty one to the power of negative start fraction two over five end fraction end power can be written in the form start fraction one over root of order cap a of forty one to the power of cap b end power end fraction. What is the value of B?

Answer 1

From the description we can infer that we have the expression: $41^{- \frac{2}{5} }$.
Now, to write our expression as a as a root, we are going to apply the law of exponents: $x^{-n}= \frac{1}{x^n}$ first
$41^{- \frac{2}{5} }= \frac{1}{41^{ \frac{2}{5} }}$

Next, we are going to apply the law about fractional exponents: $x^{ \frac{m}{n}}= \sqrt[n]{x^m}$
$\frac{1}{41^{ \frac{2}{5} }}= \frac{1}{ \sqrt[5]{41^2} }$

We can conclude that the value of B is 2.