Question

In the following exercises, simplify each expression.

$$\begin{gathered} \left(a\right).{\left(2q\right)}^{-4} \\ \left(b\right).2q^{-4} \\ \left(c\right).-2q^{-4} \end{gathered}$$

Short answer

The simplified form of the expressions

$$\begin{gathered} \left(a\right).{\left(2q\right)}^{-4}=\frac{1}{16q^4} \\ \left(b\right).2q^{-4}=\frac{2}{q^4} \\ \left(c\right).-2q^{-4}=-\frac{2}{q^4} \end{gathered}$$

Step-by-step solution

Part (a) Step 1. Given information.

The given expression is${\left(2q\right)}^{-4}.$

Part (a) Step 2. Calculate the expression.

Apply the concept of negative exponent.

${\left(ab\right)}^{-n}=\frac{1}{a^n{b}^n}$

So,

Part (b) Step 1. Given information.

The given expression is$2q^{-4}$.

Part (b) Step 2. Calculate the expression.

Apply the concept of negative exponent.

$a{b}^{-n}=\frac{a}{b^n}$

So,

$2q^{-4}=\frac{2}{q^4}$

Part (c) Step 1. Given information.

The given expression is$-2q^{-4}.$

Part (c) Step 2. Calculate the expression.

Apply the concept of negative exponent.

$-a{b}^{-n}=-\frac{a}{b^n}$

$-2q^{-4}=-\frac{2}{q^4}.$