Q. 176 - Intermediate Algebra

Question

Explain why $-5^3=(-5{)}^3$ but $-5^4\ne (-5{)}^4$

Step-by-Step Solution

Answer

This is correct only for odd exponents, for even exponents it is not correct.

Step 1 Given information

Explain why $(-5{)}^3=-5^3$but$(-5{)}^4\ne -5^4$

Step 2 Explanation

Here

$$\begin{gathered} (-5{)}^3=(-1\times 5{)}^3 \\ =(-1{)}^3\times (5{)}^3 \\ =-1\times 5^3 \\ =-5^3 \end{gathered}$$

And

$$\begin{gathered} (-5{)}^4=(-1\times 5{)}^4 \\ =(-1{)}^4\times (5{)}^4 \\ =1\times 5^4 \\ =5^4 \\ \ne -5^4 \end{gathered}$$

This is correct only for odd exponents, for even exponents it is not correct.