Question

In the following exercises, simplify each expression.

$$\begin{gathered} \left(a\right).{\left(3p\right)}^{-2} \\ \left(b\right).3p^{-2} \\ \left(c\right).-3p^{-2} \end{gathered}$$

Short answer

The simplified form of the expressions

$$\begin{gathered} \left(a\right).{\left(3p\right)}^{-2}=\frac{1}{9p^2} \\ \left(b\right).3p^{-2}=\frac{3}{p^2} \\ \left(c\right).-3p^{-2}=-\frac{3}{p^2} \end{gathered}$$

Step-by-step solution

Part (a) Step 1. Given information.

The given expression is${\left(3p\right)}^{-2}$.

Part (a) Step2. Calculate the expression.

Apply the concept of negative exponent.

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

So,

${\left(3p\right)}^{-2}=\frac{1}{9p^2}$

Part (b) Step 1.  Given information.

The given expression is$3p^{-2}.$

Part (b) Step 2. Calculate the expression.

Apply the concept of negative exponent.

$a{b}^{-1}=\frac{a}{b}$

So,

$3p^{-2}=\frac{3}{p^2}$

Part (c) Step 1. Given expression.

The given expression is$-3p^{-2}.$

Part (c) Step 2. Calculate the expression. 

Apply the concept of negative exponent.

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

So,

$-3p^{-2}=-\frac{3}{p^2}$