What is ((-5x^{-2}y^{-2}z)^2)/((10^{-1/3)x^{2/3}yz^{-2/3})^{-3}} ?

The solution to ((-5x^{-2}y^{-2}z)^2)/((10^{-1/3)x^{2/3}yz^{-2/3})^{-3}} is 5/(2x^2y)

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simplify ((-5x^{-2}y^{-2}z)^2)/((10^{-1/3)x^{2/3}yz^{-2/3})^{-3}}

simplify

\frac{( - 5 x ^{- 2} y ^{- 2} z ) ^{2}}{( 1 0 ^{- \frac{1}{3}} x ^{\frac{2}{3}} y z ^{- \frac{2}{3}} ) ^{- 3}}

\frac{5}{2 x ^{2} y}

Solution steps

\frac{( - 5 x ^{- 2} y ^{- 2} z ) ^{2}}{( 1 0 ^{- \frac{1}{3}} x ^{\frac{2}{3}} y z ^{- \frac{2}{3}} ) ^{- 3}}

Apply exponent rule:

(- a)^{n} = a^{n},

n

is even

(- 5 x^{- 2} y^{- 2} z)^{2} = (5 x^{- 2} y^{- 2} z)^{2}

= \frac{( 5 x ^{- 2} y ^{- 2} z ) ^{2}}{( 1 0 ^{- \frac{1}{3}} x ^{\frac{2}{3}} y z ^{- \frac{2}{3}} ) ^{- 3}}

Simplify

(5 x^{- 2} y^{- 2} z)^{2} : 5^{2} \cdot \frac{1}{x ^{4}} \cdot \frac{1}{y ^{4}} z^{2}

= \frac{5 ^{2} \cdot \frac{1}{x ^{4}} \cdot \frac{1}{y ^{4}} z ^{2}}{( 1 0 ^{- \frac{1}{3}} x ^{\frac{2}{3}} y z ^{- \frac{2}{3}} ) ^{- 3}}

Simplify

(1 0^{- \frac{1}{3}} x^{\frac{2}{3}} y z^{- \frac{2}{3}})^{- 3} : 10 \cdot \frac{1}{x ^{2}} y^{- 3} z^{2}

= \frac{5 ^{2} \cdot \frac{1}{x ^{4}} \cdot \frac{1}{y ^{4}} z ^{2}}{10 \cdot \frac{1}{x ^{2}} y ^{- 3} z ^{2}}

Factor the number:

10 = 5 \cdot 2

= \frac{5 ^{2} \cdot \frac{1}{x ^{4}} \cdot \frac{1}{y ^{4}} z ^{2}}{5 \cdot 2 \cdot \frac{1}{x ^{2}} y ^{- 3} z ^{2}}

\frac{5 ^{2}}{5} = 5

= \frac{5 \cdot \frac{1}{x ^{4}} \cdot \frac{1}{y ^{4}} z ^{2}}{2 \cdot \frac{1}{x ^{2}} y ^{- 3} z ^{2}}

Cancel the common factor:

z^{2}

= \frac{5 \cdot \frac{1}{x ^{4}} \cdot \frac{1}{y ^{4}}}{2 \cdot \frac{1}{x ^{2}} y ^{- 3}}

Simplify

\frac{5 \cdot \frac{1}{x ^{4}} \cdot \frac{1}{y ^{4}}}{2 \cdot \frac{1}{x ^{2}} y ^{- 3}} : \frac{5}{x ^{2} y \cdot 2}

= \frac{5}{x ^{2} y \cdot 2}

= \frac{5}{2 x ^{2} y}

\frac{5 a ^{m} ( 5 b ^{m} ) ^{2}}{( ( a ^{2} ) ^{m} ) ^{2}}

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(4 y - 3) 2

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m^{3} + 8

What is ((-5x^{-2}y^{-2}z)^2)/((10^{-1/3)x^{2/3}yz^{-2/3})^{-3}} ?
The solution to ((-5x^{-2}y^{-2}z)^2)/((10^{-1/3)x^{2/3}yz^{-2/3})^{-3}} is 5/(2x^2y)