Q. 150 - Intermediate Algebra

Question

In the following exercises, simplify. 

(a) $-{64}^{\frac{3}{2}}$

(b) $-{64}^{-\frac{3}{2}}$

(c) ${\left(-64\right)}^{\frac{3}{2}}$

Step-by-Step Solution

Answer

(a) The answer is $-512$

(b) The answer is $-\frac{1}{512}$

(c) The answer is Not real solution.

Step 1. Part (a) Simplify the expression - 64 3 2

$$\begin{gathered} -{\left(64\right)}^{\frac{3}{2}} \\ =-{\left(\sqrt{64}\right)}^3 \\ =-{\left(8\right)}^3 \\ =-512 \end{gathered}$$

Step 2. Part (b) Simplify the expression - 64 - 3 2

$$\begin{gathered} -{\left(64\right)}^{-\frac{3}{2}} \\ =-{\left(\sqrt{64}\right)}^{-3} \\ =-{\left(8\right)}^{-3} \\ =-\frac{1}{8^3} \\ =-\frac{1}{512} \end{gathered}$$

Step 3. Part (c) Simplify the expression - 64 3 2

$$\begin{gathered} {\left(-64\right)}^{\frac{3}{2}} \\ ={\left(\sqrt{-64}\right)}^3 \end{gathered}$$

This is not a real solution.