### Home > CCA2 > Chapter 2 > Lesson 2.1.2 > Problem2-19

2-19.

Simplify each of the following expressions. Be sure that your answer has no negative or fractional exponents.

1. $\left(\frac{1}{81}\right)^{-1/4}$

Begin by rewriting the expression as $\left(\left(\frac{1}{81}\right)^{-1}\right)^{\frac{1}{4}}$.

Since$\left(\frac{1}{81}\right)^{-1}=81$, the expression can be rewritten as $(81)^\frac{1}{4}$.

1. $x^{−2}y^{−4}$

The negative exponents mean you will be finding the reciprocals of the factors.

1. $(2x)^{−2}(16x^2y)^{1/2}$

There are several ways to simplify this expression. Here is one:

$\frac{1}{(2x)^{2}}(16)^{\frac{1}{2}}(x^{2})^{\frac{1}{2}}(y)^{\frac{1}{2}}$

$\frac{1}{4x^2}(4)(x)(y)^{\frac{1}{2}}$

$\frac{(y)^{\frac{1}{2}}}{x}$  or $\frac{\sqrt{y}}{x}$