수와 연산 전체 문제

In the following exercises, simplify using absolute value signs as needed.

ⓐ $\sqrt{96{r}^{3}{s}^{3}}$ ⓑ $\sqrt[3]{80{x}^{7}{y}^{6}}$ ⓒ $\sqrt[4]{80{x}^{8}{y}^{9}}$

In the following exercises, simplify using absolute value signs as needed.

ⓐ $\sqrt[5]{-32}$ ⓑ $\sqrt[8]{-1}$

In the following exercises, simplify using absolute value signs as needed.

ⓐ $8+\sqrt{96}$ ⓑ $\frac{2+\sqrt{40}}{2}$

Use the Quotient Property to Simplify Radical Expressions

In the following exercises, use the Quotient Property to simplify square roots.

ⓐ $\sqrt{\frac{72}{98}}$ ⓑ $\sqrt[3]{\frac{24}{81}}$ ⓒ $\sqrt[4]{\frac{6}{96}}$

Use the Quotient Property to Simplify Radical Expressions

In the following exercises, use the Quotient Property to simplify square roots.

ⓐ $\sqrt{\frac{{y}^{4}}{{y}^{8}}}$ ⓑ $\sqrt[5]{\frac{{u}^{21}}{{u}^{11}}}$ ⓒ $\sqrt[6]{\frac{{v}^{30}}{{v}^{12}}}$

Use the Quotient Property to Simplify Radical Expressions

In the following exercises, use the Quotient Property to simplify square roots.

$\sqrt{\frac{300{m}^{5}}{64}}$

Use the Quotient Property to Simplify Radical Expressions

In the following exercises, use the Quotient Property to simplify square roots.

ⓐ $\sqrt{\frac{28{p}^{7}}{{q}^{2}}}$ ⓑ $\sqrt[3]{\frac{81{s}^{8}}{{t}^{3}}}$ ⓒ $\sqrt[4]{\frac{64{p}^{15}}{{q}^{12}}}$

Use the Quotient Property to Simplify Radical Expressions

In the following exercises, use the Quotient Property to simplify square roots.

ⓐ $\sqrt{\frac{27{p}^{2}q}{108{p}^{4}{q}^{3}}}$ ⓑ $\sqrt[3]{\frac{16{c}^{5}{d}^{7}}{250{c}^{2}{d}^{2}}}$ ⓒ $\sqrt[6]{\frac{2{m}^{9}{n}^{7}}{128{m}^{3}n}}$

Use the Quotient Property to Simplify Radical Expressions

In the following exercises, use the Quotient Property to simplify square roots.

ⓐ $\frac{\sqrt{80{q}^{5}}}{\sqrt{5q}}$ ⓑ $\frac{\sqrt[3]{-625}}{\sqrt[3]{5}}$ ⓒ $\frac{\sqrt[4]{80{m}^{7}}}{\sqrt[4]{5m}}$

Simplify expressions with ${a}^{\frac{1}{n}}$

In the following exercises, write as a radical expression.

ⓐ ${r}^{\frac{1}{2}}$ ⓑ ${s}^{\frac{1}{3}}$ ⓒ ${t}^{\frac{1}{4}}$

In the following exercises, write with a rational exponent.

ⓐ $\sqrt{21p}$ ⓑ $\sqrt[4]{8q}$ ⓒ $4\sqrt[6]{36r}$

In the following exercises, simplify.

ⓐ ${625}^{\frac{1}{4}}$ ⓑ ${243}^{\frac{1}{5}}$ ⓒ ${32}^{\frac{1}{5}}$

In the following exercises, simplify.

ⓐ ${(-1,000)}^{\frac{1}{3}}$ ⓑ $-{1,000}^{\frac{1}{3}}$ ⓒ ${(1,000)}^{-\frac{1}{3}}$

In the following exercises, simplify.

ⓐ ${(-32)}^{\frac{1}{5}}$ ⓑ ${(243)}^{-\frac{1}{5}}$ ⓒ $-{125}^{\frac{1}{3}}$

Simplify Expressions with ${a}^{\frac{m}{n}}$

In the following exercises, write with a rational exponent.

ⓐ $\sqrt[4]{{r}^{7}}$ ⓑ ${\left(\sqrt[5]{2pq}\right)}^{3}$ ⓒ $\sqrt[4]{{\left(\frac{12m}{7n}\right)}^{3}}$

In the following exercises, simplify.

ⓐ ${25}^{\frac{3}{2}}$ ⓑ ${9}^{-\frac{3}{2}}$ ⓒ ${(-64)}^{\frac{2}{3}}$

In the following exercises, simplify.

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

Use the Laws of Exponents to Simplify Expressions with Rational Exponents

In the following exercises, simplify.

ⓐ ${6}^{\frac{5}{2}}\cdot {6}^{\frac{1}{2}}$ ⓑ ${({b}^{15})}^{\frac{3}{5}}$ ⓒ $\frac{{w}^{\frac{2}{7}}}{{w}^{\frac{9}{7}}}$

Use the Laws of Exponents to Simplify Expressions with Rational Exponents

In the following exercises, simplify.

ⓐ $\frac{{a}^{\frac{3}{4}}\cdot {a}^{-\frac{1}{4}}}{{a}^{-\frac{10}{4}}}$ ⓑ ${\left(\frac{27{b}^{\frac{2}{3}}{c}^{-\frac{5}{2}}}{{b}^{-\frac{7}{3}}{c}^{\frac{1}{2}}}\right)}^{\frac{1}{3}}$

Add and Subtract Radical Expressions

In the following exercises, simplify.

ⓐ $7\sqrt{2}-3\sqrt{2}$ ⓑ $7\sqrt[3]{p}+2\sqrt[3]{p}$ ⓒ $5\sqrt[3]{x}-3\sqrt[3]{x}$