9.8 Rational exponents  (Page 6/7)

$\frac{\sqrt{75}}{10}$

$\frac{2-\sqrt{12}}{6}$

$\frac{\sqrt{48}}{\sqrt{27}}$

$\frac{\sqrt{75x^7}}{\sqrt{3x^3}}$

$\frac{\sqrt{20y^5}}{\sqrt{2y}}$

$\frac{\sqrt{98p^6{q}^4}}{\sqrt{2p^4{q}^8}}$

$\frac{10}{\sqrt{15}}$

$\frac{6}{\sqrt{6}}$

$\frac{5}{3\sqrt{5}}$

$\frac{10}{2\sqrt{6}}$

$\sqrt{\frac{3}{28}}$

$\sqrt{\frac{9}{75}}$

$\frac{4}{4+\sqrt{27}}$

$\frac{5}{2-\sqrt{10}}$

$\frac{4}{2-\sqrt{5}}$

$\frac{5}{4-\sqrt{8}}$

$\frac{\sqrt{2}}{\sqrt{p}+\sqrt{3}}$

$\frac{\sqrt{x}-\sqrt{2}}{\sqrt{x}+\sqrt{2}}$

$\sqrt{7z+1}=6$

$\sqrt{4u-2}-4=0$

$\sqrt{6m+4}-5=0$

$\sqrt{2u-3}+2=0$

$\sqrt{u-4}+4=u$

$\sqrt{v-9}+9=0$

$\sqrt{r-4}-r=\mathrm{-10}$

$\sqrt{s-9}-s=\mathrm{-9}$

$2\sqrt{2x-7}-4=8$

$\sqrt{2-x}=\sqrt{2x-7}$

$\sqrt{a}+3=\sqrt{a+9}$

$\sqrt{r}+3=\sqrt{r+4}$

$\sqrt{u}+2=\sqrt{u+5}$

$\sqrt{n+11}-1=\sqrt{n+4}$

$\sqrt{y+5}+1=\sqrt{2y+3}$

A pallet of sod will cover an area of about 600 square feet. Trinh wants to order a pallet of sod to make a square lawn in his backyard. Use the formula $s=\sqrt{A}$ to find the length of each side of his lawn.

A helicopter dropped a package from a height of 900 feet above a stranded hiker. Use the formula $t=\frac{\sqrt{h}}{4}$ to find how many seconds it took for the package to reach the hiker.

Officer Morales measured the skid marks of one of the cars involved in an accident. The length of the skid marks was 245 feet. Use the formula $s=\sqrt{24d}$ to find the speed of the car before the brakes were applied.

ⓐ $\sqrt[6]{64}$
ⓑ $\sqrt[3]{64}$

ⓐ $\sqrt[3]{\mathrm{-27}}$
ⓑ $\sqrt[4]{\mathrm{-64}}$

ⓐ $\sqrt[9]{d^9}$
ⓑ $\sqrt[8]{v^8}$

ⓐ $\sqrt[5]{a^{10}}$
ⓑ $\sqrt[3]{b^{27}}$

ⓐ $\sqrt[4]{16x^8}$
ⓑ $\sqrt[6]{64y^{12}}$

ⓐ $\sqrt[7]{128r^{14}}$
ⓑ $\sqrt[4]{81s^{24}}$

ⓐ $\sqrt[9]{d^9}$
ⓑ

ⓐ $\sqrt[3]{54}$
ⓑ $\sqrt[4]{128}$

ⓐ $\sqrt[5]{64c^8}$
ⓑ $\sqrt[4]{48d^7}$

ⓐ $\sqrt[3]{343q^7}$
ⓑ $\sqrt[6]{192r^9}$

ⓐ $\sqrt[3]{\mathrm{-500}}$
ⓑ $\sqrt[4]{\mathrm{-16}}$

$\sqrt[5]{\frac{r^{10}}{r^5}}$

$\sqrt[3]{\frac{w^{12}}{w^2}}$

$\sqrt[4]{\frac{64y^8}{4y^5}}$

$\sqrt[3]{\frac{54z^9}{2z^3}}$

$\sqrt[6]{\frac{64a^7}{b^2}}$

$4\sqrt[5]{20}-2\sqrt[5]{20}$

$4\sqrt[3]{18}+3\sqrt[3]{18}$

$\sqrt[4]{1250}-\sqrt[4]{162}$

$\sqrt[3]{640c^5}-\sqrt[3]{\mathrm{-80}{c}^3}$

$\sqrt[5]{96t^8}+\sqrt[5]{486t^4}$

$r^{\frac{1}{8}}$

$s^{\frac{1}{10}}$

$\sqrt[5]{u}$

$\sqrt[6]{v}$

$\sqrt[3]{9m}$

$\sqrt[6]{10z}$

${16}^{\frac{1}{4}}$

${32}^{\frac{1}{5}}$

${\left(\mathrm{-125}\right)}^{\frac{1}{3}}$

${\left(125\right)}^{-\frac{1}{3}}$

${\left(\mathrm{-9}\right)}^{\frac{1}{2}}$

${\left(36\right)}^{-\frac{1}{2}}$

$\sqrt[3]{q^5}$

$\sqrt[5]{n^8}$

${27}^{-\frac{2}{3}}$

${64}^{\frac{5}{2}}$

${36}^{\frac{3}{2}}$

${81}^{-\frac{5}{2}}$

$3^{\frac{4}{5}}·3^{\frac{6}{5}}$

${\left(x^6\right)}^{\frac{4}{3}}$

$\frac{z^{\frac{5}{2}}}{z^{\frac{7}{5}}}$

${\left(16s^{\frac{9}{4}}\right)}^{\frac{1}{4}}$

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

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

$\sqrt{81+144}$

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

${\left(27s^{\frac{3}{5}}\right)}^{\frac{1}{3}}$

A helicopter flying at an altitude of 600 feet dropped a package to a lifeboat. Use the formula $t=\frac{\sqrt{h}}{4}$ to find how many seconds it took for the package to reach the hiker. Round your answer to the nearest tenth of a second.