What is (x^2y^-3)/z ((3x^0)/(zy^2))^{-2} ?

The solution to (x^2y^-3)/z ((3x^0)/(zy^2))^{-2} is (x^2y^4z)/3

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simplify (x^2y^-3)/z ((3x^0)/(zy^2))^{-2}

simplify

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

\frac{x ^{2} y ^{4} z}{3}

Solution steps

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

Apply exponent rule:

a^{- b} = \frac{1}{a ^{b}}

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

Apply rule

a^{0} = 1, a \neq = 0

x^{0} = 1

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

\frac{1}{( \frac{3 \cdot 1}{z y ^{2}} ) ^{2}} = \frac{y ^{4} z ^{2}}{3 ^{2}}

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

Multiply fractions:

\frac{a}{b} \cdot \frac{c}{d} = \frac{a \cdot c}{b \cdot d}

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

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

= \frac{3 x ^{2} z ^{2} y ^{4}}{3 ^{2} z}

Cancel the common factor:

3

= \frac{x ^{2} z ^{2} y ^{4}}{3 z}

Cancel the common factor:

z

= \frac{x ^{2} z y ^{4}}{3}

8765 e^{- 2}

e^{- \frac{1}{x ^{2} + y ^{2}}}

\frac{1}{2} a^{6} b^{4} c^{8} e n t re \frac{4}{3} a^{2} b c

20 t e^{- 10} \cdot 100

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

What is (x^2y^-3)/z ((3x^0)/(zy^2))^{-2} ?
The solution to (x^2y^-3)/z ((3x^0)/(zy^2))^{-2} is (x^2y^4z)/3