Question

In the following exercises, simplify.

(a)${100}^{\frac{3}{2}}$

(b)${49}^{-\frac{5}{2}}$

(c)${\left(-100\right)}^{\frac{3}{2}}$

Short answer

(a) The answer is$1000$

(b) The answer is$\frac{1}{19807}$

(c) The answer is Not real solution.

Step-by-step solution

Step 1. Part (a) Simplify the expression 10032

We will use the property

$a^{\frac{m}{n}}=(\sqrt[n]{a}{)}^m$and $a^{\frac{m}{n}}=\sqrt[n]{a^m}$

$$\begin{gathered} {100}^{\frac{3}{2}} \\ ={10}^{2\times \frac{3}{2}} \\ ={10}^3 \\ =1000 \end{gathered}$$

Step 2. Part (b) Simplify the expression 49-52

$$\begin{gathered} {49}^{-\frac{5}{2}} \\ =7^{2\times -\frac{5}{2}} \\ =7^{-5} \\ =\frac{1}{7^5} \\ =\frac{1}{19807} \end{gathered}$$

Step 3. Part (c) Simplify the expression -10032

$$\begin{gathered} {\left(-100\right)}^{\frac{3}{2}} \\ ={\left(\sqrt{-100}\right)}^3 \end{gathered}$$

This is not real solution.