Question

In the following exercises, simplify each expression using the Product to a Power Property.

(a) (-4ab)²

(b) (5x)⁰

(c) (4y³)^-3

(d) (-7y^-3)²

Short answer

The simplified form of the given expression is :-

$$\begin{gathered} \left(a\right)16a^2{b}^2 \\ \left(b\right)1 \\ \left(c\right)\frac{1}{64y^9} \\ \left(d\right)49y^{-6} \end{gathered}$$

Step-by-step solution

Part (a) Step 1. Given information.

The given expression is${(-4ab)}^2$.

Part (a). Step 2. Apply the power rule.

Here we use the concept of power rule,

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

So,

${(-4ab)}^2=16a^2{b}^2.$

Part (b) Step 1. Given information.

The given expression is ${\left(5x\right)}^0.$

part (b). Step2. Apply the concept.

Here we apply the concept of anything raised to zero is $1$.

So,

${\left(5x\right)}^0=1.$

Part (c) Step 1. Given information.

The given expression is${\left(4y^3\right)}^{-3}.$

Part (c) Step 2. We apply the concept.

In this expression we use negative exponents rule that is-

$b^{-n}=\frac{1}{b^n}.$

Our final expression is$\frac{1}{64y^9}.$

Part (d) step 1. Given information.

The given expression is${(-7y^{-3})}^2.$

Part (d) Step 2. Apply the concept.

We use the concept of negative exponents.

${(-ab)}^2=a^2{b}^2.$

So,

${(-7y^{-3})}^2=49y^{-6}$