91Ó°ÊÓ

In the following exercise, simplify.

(a)$\sqrt[3]{-64}$

(b)$\sqrt[4]{-16}$

(c)$\sqrt[5]{-243}$

In the following exercises,simplify

$$\begin{gathered} \left(a\right)\frac{a^{{\displaystyle \frac{3}{4}}}.a^{-{\displaystyle \frac{1}{4}}}}{a^{-{\displaystyle \frac{10}{4}}}} \\ \left(b\right){\left(\frac{27b^{{\displaystyle \frac{2}{3}}}.c^{-{\displaystyle \frac{5}{2}}}}{b^{-{\displaystyle \frac{7}{3}}}.c^{{\displaystyle \frac{1}{2}}}}\right)}^{\frac{1}{3}} \end{gathered}$$

In the following exercises,simplify

$$\begin{gathered} \left(a\right)\frac{c^{{\displaystyle \frac{5}{3}}}.c^{-{\displaystyle \frac{1}{3}}}}{c^{-{\displaystyle \frac{2}{3}}}} \\ \left(b\right){\left(\frac{8x^{{\displaystyle \frac{5}{3}}}.y^{-{\displaystyle \frac{1}{2}}}}{27x^{-{\displaystyle \frac{4}{3}}}.y^{{\displaystyle \frac{5}{2}}}}\right)}^{\frac{1}{3}} \end{gathered}$$

In the following exercises,simplify

$$\begin{gathered} \left(a\right)\frac{m^{{\displaystyle \frac{7}{4}}}.m^{-{\displaystyle \frac{5}{4}}}}{m^{-{\displaystyle \frac{2}{4}}}} \\ \left(b\right){\left(\frac{16m^{{\displaystyle \frac{1}{5}}}.n^{{\displaystyle \frac{3}{2}}}}{81m^{{\displaystyle \frac{9}{5}}}.n^{-{\displaystyle \frac{1}{2}}}}\right)}^{\frac{1}{4}} \end{gathered}$$

Explain why the expression ${(−16)}^{\frac{3}{2}}$cannot be evaluated.

Add and subtract radical expressions in the following exercises, simplify.

(a)$8\sqrt{2}-5\sqrt{2}$

(b)$5\sqrt[3]{m}+2\sqrt[3]{m}$

(c)$8\sqrt[4]{m}-2\sqrt[4]{m}$

Add and subtract radical expressions in the following exercises, simplify.

(a)$7\sqrt{2}-3\sqrt{2}$

(b)$7\sqrt[3]{p}+2\sqrt[3]{p}$

(c)$5\sqrt[3]{x}-3\sqrt[3]{x}$

Add and subtract radical expressions in the following exercises, simplify.

(a)$3\sqrt{5}+6\sqrt{5}$

(b)$9\sqrt[3]{a}+3\sqrt[3]{a}$

(c)$5\sqrt[4]{2z}+\sqrt[4]{2z}$

Add and subtract radical expressions in the following exercises, simplify.

(a)$4\sqrt{5}+8\sqrt{5}$

(b)$\sqrt[3]{m}-4\sqrt[3]{m}$

(c)$\sqrt{n}+3\sqrt{n}$

Add and subtract radical expressions in the following exercises, simplify.

(a) $3\sqrt{2a}-4\sqrt{2a}+5\sqrt{2a}$

(b)$5\sqrt[4]{3ab}-3\sqrt[4]{3ab}-2\sqrt[4]{ab}$