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Practice Solutions

Simplify. Write expressions with positive exponents only.

$\frac{p^{- 2} q^{- 4}}{4 r^{- \frac{1}{2}}}$

$\frac{r^{\frac{1}{2}}}{4 p^{2} q^{4}}$

$(15 x^{5} y) (4 x^{3} y^{2})$

$(15) (4) x^{5 + 3} y^{1 + 2} = 60 x^{8} y^{3}$

$\frac{x^{0} y^{3}}{2^{3}}$
$\frac{(1) y^{3}}{8} = \frac{y^{3}}{8}$

${(\frac{2 x^{5}}{3})}^{3}$

$\frac{2^{3} x^{15}}{3^{3}} = \frac{8 x^{15}}{27}$

$\frac{3^{- 1} a^{- 5} b^{2}}{5 c^{6} d}$

$\frac{b^{2}}{5 (3) a^{5} c^{6} d} = \frac{b^{2}}{15 a^{5} c^{6} d}$

$(10 x^{2} y) (\frac{1}{2} x^{9} y^{- 4}) (4 x y^{3})$

$(10) (\frac{1}{2}) (4) x^{2 + 9 + 1} y^{1 + - 4 + 3} = 20 x^{12} y^{0} = 20 x^{12}$

Simplify. Write expressions with positive exponents only.

$\frac{3^{2} x^{- 6}}{2^{- 1} x^{3}}$

$\frac{3^{2} (2)}{x^{3 + 6}} = \frac{9 (2)}{x^{9}} = \frac{18}{x^{9}}$

${(\frac{4 x^{- 6} y}{5 z^{5}})}^{- 2}$

$\frac{4^{- 2} x^{12} y^{- 2}}{5^{- 2} z^{- 10}} = \frac{5^{2} x^{12} z^{10}}{4^{2} y^{2}} = \frac{25 x^{12} z^{10}}{16 y^{2}}$

$(\frac{a^{18} b^{- 3}}{a^{9} b^{6}}) (\frac{a^{4} b^{- 5}}{a^{11} b^{7}})$

$\frac{a^{18 + 4} b^{- 3 + - 5}}{a^{9 + 11} b^{6 + 7}} = \frac{a^{22} b^{- 8}}{a^{20} b^{13}} = \frac{a^{22 - 20}}{b^{13 - (- 8)}} = \frac{a^{2}}{b^{21}}$

${(9 x y z)}^{2} (\frac{x^{4} z^{- 7}}{3 y^{8}})$

$9^{2} x^{2} y^{2} z^{2} (\frac{x^{4}}{3 y^{8} z^{7}}) = \frac{81 x^{2 + 4}}{3 y^{8 - 2} z^{7 - 2}} = \frac{27 x^{6}}{y^{6} z^{5}}$

$(\frac{5^{- 1} x^{3}}{y^{4} z^{- 5}}) {(\frac{z^{5}}{x^{4}})}^{2}$

$(\frac{x^{3} z^{5}}{5 y^{4}}) (\frac{z^{10}}{x^{8}}) = \frac{z^{5 + 10}}{5 x^{8 - 3} y^{4}} = \frac{z^{15}}{5 x^{5} y^{4}}$

$(\frac{10^{- 1} b^{3}}{3 a^{2} c^{- 4}}) (\frac{a^{5} b^{- 3}}{3^{- 2} c})$

$\frac{10^{- 1} a^{5 - 2} b^{3 + - 3}}{3^{1 + - 2} c^{- 4 + 1}} = \frac{10^{- 1} a^{3} b^{0}}{3^{- 1} c^{- 3}} = \frac{3 a^{3} c^{3}}{10}$