Question

Simplify the following expression to simplest form using only positive exponents. 1

Answer 1

For this problem, we need to simplify a certain expression using only positive exponents.

The expression is given below:

$(16x^{-32}y^{-12})^{\frac{5}{4}}$

The first step is to multiply the exponent that is outside of the parenthesis with the ones inside the parenthesis.

$\begin{gathered} 16^{\frac{5}{4}}x^{\frac{-32\cdot5}{4}}y^{\frac{-12\cdot5}{4}}\\ \\ 16^{\frac{5}{4}}x^{-40}y^{-15} \end{gathered}$

Now we need to invert the two bases, to make the exponents positive:

$\begin{gathered} \frac{16^{\frac{5}{4}}}{x^{40}y^{15}}\\ \\ \frac{\sqrt[4]{16^5}}{x^{40}y^{15}}\\ \\ \frac{32}{x^{40}y^{15}} \end{gathered}$