Question

In the following exercises, simplify each expression.

$$\begin{gathered} \left(\text{a}\right){\left(-7\right)}^3 \\ \left(\text{b}\right)-7^3 \end{gathered}$$

Short answer

The simplified expressions are

$$\begin{gathered} \left(\text{a}\right){\left(-7\right)}^3=-343 \\ \left(\text{b}\right)-7^3=-343 \end{gathered}$$

Step-by-step solution

Step 1. Given information

The given expressions are

$$\begin{gathered} \left(\text{a}\right){\left(-7\right)}^3 \\ \left(\text{b}\right)-7^3 \end{gathered}$$

Part a.Step 1. Simplify the expression

$$\begin{gathered} \left(\text{a}\right) \\ {\left(-7\right)}^3=\left(-7\right)\times \left(-7\right)\times \left(-7\right)\text{Expandtheproduct} \\ =49\times \left(-7\right)\text{Simplify} \\ =-343 \end{gathered}$$

Hence,${\left(-7\right)}^3=-343$

Part b.Step 1.Simplify the expression

$$\begin{gathered} \left(\text{b}\right) \\ -7^3=-\left(7\times 7\times 7\right)\text{Expandtheproduct} \\ =-\left(343\right)\text{Simplify} \\ =-343 \end{gathered}$$

Hence,$-7^3=-343.$