수와 연산 전체 문제

Use the Laws of Exponents to Simplify Expressions with Rational Exponents

In the following exercises, simplify.

${({m}^{8}{n}^{12})}^{\frac{1}{4}}$

Use the Laws of Exponents to Simplify Expressions with Rational Exponents

In the following exercises, simplify.

$\frac{{z}^{\frac{2}{3}}\cdot {z}^{-\frac{1}{3}}}{{z}^{-\frac{5}{3}}}$

In the following exercises, simplify.

$\sqrt{81+144}$

In the following exercises, simplify.

$\sqrt{169{m}^{4}{n}^{2}}$

In the following exercises, simplify.

$\sqrt{36{n}^{13}}$

In the following exercises, simplify.

$3\sqrt{13}+5\sqrt{2}+\sqrt{13}$

In the following exercises, simplify.

$5\sqrt{20}+2\sqrt{125}$

In the following exercises, simplify.

$\left(3\sqrt{6y}\right)\left(2\sqrt{50{y}^{3}}\right)$

In the following exercises, simplify.

$\left(2-5\sqrt{x}\right)\left(3+\sqrt{x}\right)$

In the following exercises, simplify.

${\left(1-2\sqrt{q}\right)}^{2}$

In the following exercises, simplify.

ⓐ $\sqrt[4]{{a}^{12}}$ ⓑ $\sqrt[3]{{b}^{21}}$

In the following exercises, simplify.

ⓐ $\sqrt[4]{81{x}^{12}}$ ⓑ $\sqrt[6]{64{y}^{18}}$

In the following exercises, simplify.

$\sqrt{\frac{64{r}^{12}}{25{r}^{6}}}$

In the following exercises, simplify.

$\sqrt{\frac{14{y}^{3}}{7y}}$

In the following exercises, simplify.

$\frac{\sqrt[5]{256{x}^{7}}}{\sqrt[5]{4{x}^{2}}}$

In the following exercises, simplify.

$\sqrt[4]{512}-2\sqrt[4]{32}$

In the following exercises, simplify.

ⓐ ${256}^{\frac{1}{4}}$ ⓑ ${243}^{\frac{1}{5}}$

In the following exercises, simplify.

${49}^{\frac{3}{2}}$

In the following exercises, simplify.

${25}^{-\frac{5}{2}}$

In the following exercises, simplify.

$\frac{{w}^{\frac{3}{4}}}{{w}^{\frac{7}{4}}}$