9.8 Rational exponents  (Page 5/7)

ⓐ ${\left(x^8{y}^{10}\right)}^{\frac{1}{2}}$
ⓑ ${\left(a^9{b}^{12}\right)}^{\frac{1}{3}}$

ⓐ ${\left(r^8{s}^4\right)}^{\frac{1}{4}}$
ⓑ ${\left(u^{15}{v}^{20}\right)}^{\frac{1}{5}}$

ⓐ ${\left(a^6{b}^{16}\right)}^{\frac{1}{2}}$
ⓑ ${\left(j^9{k}^6\right)}^{\frac{2}{3}}$

ⓐ ${\left(r^{16}{s}^{10}\right)}^{\frac{1}{2}}$
ⓑ ${\left(u^{10}{v}^5\right)}^{\frac{4}{5}}$

ⓐ $\frac{r^{\frac{5}{2}}·r^{-\frac{1}{2}}}{r^{-\frac{3}{2}}}$
ⓑ $\frac{s^{\frac{1}{5}}·s}{s^{-\frac{9}{5}}}$

ⓐ $\frac{a^{\frac{3}{4}}·a^{-\frac{1}{4}}}{a^{-\frac{10}{4}}}$
ⓑ $\frac{b^{\frac{2}{3}}·b}{b^{-\frac{7}{3}}}$

ⓐ $\frac{c^{\frac{5}{3}}·c^{-\frac{1}{3}}}{c^{-\frac{2}{3}}}$
ⓑ $\frac{d^{\frac{3}{5}}·d}{d^{-\frac{2}{5}}}$

ⓐ $\frac{m^{\frac{7}{4}}·m^{-\frac{5}{4}}}{m^{-\frac{2}{4}}}$
ⓑ $\frac{n^{\frac{3}{7}}·n}{n^{-\frac{4}{7}}}$

$4^{\frac{5}{2}}·4^{\frac{1}{2}}$

$n^{\frac{2}{6}}·n^{\frac{4}{6}}$

${\left(a^{24}\right)}^{\frac{1}{6}}$

${\left(b^{10}\right)}^{\frac{3}{5}}$

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

$\frac{z^{\frac{2}{3}}}{z^{\frac{8}{3}}}$

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

${\left(64s^{\frac{3}{5}}\right)}^{\frac{1}{6}}$

${\left(r^9{s}^{12}\right)}^{\frac{1}{3}}$

${\left(u^{12}{v}^{18}\right)}^{\frac{1}{6}}$

Landscaping Joe wants to have a square garden plot in his backyard. He has enough compost to cover an area of 144 square feet. Simplify ${144}^{\frac{1}{2}}$ to find the length of each side of his garden.

Landscaping Elliott wants to make a square patio in his yard. He has enough concrete to pave an area of 242 square feet. Simplify ${242}^{\frac{1}{2}}$ to find the length of each side of his patio.Round to the nearest tenth of a foot.

Gravity While putting up holiday decorations, Bob dropped a decoration from the top of a tree that is 12 feet tall. Simplify $\frac{{12}^{\frac{1}{2}}}{{16}^{\frac{1}{2}}}$ to find how many seconds it took for the decoration to reach the ground. Round to the nearest tenth of a second.

Gravity An airplane dropped a flare from a height of 1024 feet above a lake. Simplify $\frac{{1024}^{\frac{1}{2}}}{{16}^{\frac{1}{2}}}$ to find how many seconds it took for the flare to reach the water.

Show two different algebraic methods to simplify $4^{\frac{3}{2}}.$ Explain all your steps.

Explain why the expression ${\left(\mathrm{-16}\right)}^{\frac{3}{2}}$ cannot be evaluated.

$\sqrt{64}$

$\sqrt{144}$

$-\sqrt{25}$

$-\sqrt{81}$

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

$\sqrt{\mathrm{-36}}$

$\sqrt{64}+\sqrt{225}$

$\sqrt{64+225}$

$\sqrt{28}$

$\sqrt{155}$

$\sqrt{15}$

$\sqrt{57}$

$\sqrt{q^2}$

$\sqrt{64b^2}$

$\text{−}\sqrt{121a^2}$

$\sqrt{225m^2{n}^2}$

$\text{−}\sqrt{100q^2}$

$\sqrt{49y^2}$

$\sqrt{4a^2{b}^2}$

$\sqrt{121c^2{d}^2}$

$\sqrt{300}$

$\sqrt{98}$

$\sqrt{x^{13}}$

$\sqrt{y^{19}}$

$\sqrt{16m^4}$

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

$\sqrt{288m^{21}}$

$\sqrt{150n^7}$

$\sqrt{48r^5{s}^4}$

$\sqrt{108r^5{s}^3}$

$\frac{10-\sqrt{50}}{5}$

$\frac{6+\sqrt{72}}{6}$

$\sqrt{\frac{16}{25}}$

$\sqrt{\frac{81}{36}}$

$\sqrt{\frac{x^8}{x^4}}$

$\sqrt{\frac{y^6}{y^2}}$

$\sqrt{\frac{98p^6}{2p^2}}$

$\sqrt{\frac{72q^8}{2q^4}}$

$\sqrt{\frac{65}{121}}$

$\sqrt{\frac{26}{169}}$

$\sqrt{\frac{64x^4}{25x^2}}$

$\sqrt{\frac{36r^{10}}{16r^5}}$

$\sqrt{\frac{48p^3{q}^5}{27pq}}$

$\sqrt{\frac{12r^5{s}^7}{75r^{2}s}}$

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

$5\sqrt{5}+7\sqrt{5}$

$4\sqrt{y}+4\sqrt{y}$

$6\sqrt{m}-2\sqrt{m}$

$\mathrm{-3}\sqrt{7}+2\sqrt{7}-\sqrt{7}$

$8\sqrt{13}+2\sqrt{3}+3\sqrt{13}$

$3\sqrt{5xy}-\sqrt{5xy}+3\sqrt{5xy}$

$2\sqrt{3rs}+\sqrt{3rs}-5\sqrt{rs}$

$\sqrt{32}+3\sqrt{2}$

$\sqrt{8}+3\sqrt{2}$

$\sqrt{72}+\sqrt{50}$

$\sqrt{48}+\sqrt{75}$

$3\sqrt{32}+\sqrt{98}$

$\frac{1}{3}\sqrt{27}-\frac{1}{8}\sqrt{192}$

$\sqrt{50y^5}-\sqrt{72y^5}$

$6\sqrt{18n^4}-3\sqrt{8n^4}+n^2\sqrt{50}$

$\sqrt{2}·\sqrt{20}$

$2\sqrt{2}·6\sqrt{14}$

$\sqrt{2m^2}·\sqrt{20m^4}$

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

$\left(6\sqrt{3v^4}\right)\left(5\sqrt{30v}\right)$

${\left(\sqrt{8}\right)}^2$

${\left(\text{−}\sqrt{10}\right)}^2$

$\left(2\sqrt{5}\right)\left(5\sqrt{5}\right)$

$\left(\mathrm{-3}\sqrt{3}\right)\left(5\sqrt{18}\right)$

$10(2-\sqrt{7})$

$\sqrt{3}\left(4+\sqrt{12}\right)$

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

$\left(5-3\sqrt{7}\right)\left(1-2\sqrt{7}\right)$

$\left(1-3\sqrt{x}\right)\left(5+2\sqrt{x}\right)$

$\left(3+4\sqrt{y}\right)\left(10-\sqrt{y}\right)$

${\left(1+6\sqrt{p}\right)}^2$

${\left(2-6\sqrt{5}\right)}^2$

$\left(3+2\sqrt{7}\right)\left(3-2\sqrt{7}\right)$

$\left(6-\sqrt{11}\right)\left(6+\sqrt{11}\right)$