Q. 149 - Intermediate Algebra

Question

In the following exercises, simplify. 

(a) $-9^{\frac{3}{2}}$

(b) $-9^{-\frac{3}{2}}$

(c) ${\left(-9\right)}^{\frac{3}{2}}$

Step-by-Step Solution

Answer

(a) The answer is $-27$

(b) The answer is $-\frac{1}{27}$

(c) The answer is Not real solution.

Step 1. Part (a) Simplify the expression - 9 3 2

$$\begin{gathered} -{\left(9\right)}^{\frac{3}{2}} \\ =-{\left(\sqrt{9}\right)}^3 \\ =-{\left(3\right)}^3 \\ =-27 \end{gathered}$$

Step 2. Part (b) Simplify the expression - 9 - 3 2

$$\begin{gathered} -{\left(9\right)}^{-\frac{3}{2}}=-{\left(\sqrt{9}\right)}^{-3} \\ =-{\left(3\right)}^{-3} \\ =-\frac{1}{3^3} \\ =-\frac{1}{27} \end{gathered}$$

Step 3. Part (c) Simplify the expression - 9 3 2

$$\begin{gathered} {\left(-9\right)}^{\frac{3}{2}} \\ {\left(\sqrt{-9}\right)}^3 \end{gathered}$$

This is not a real solution.