What is ((3x^{-2}y^2)/(z^4))^{1/4} ?

The solution to ((3x^{-2}y^2)/(z^4))^{1/4} is (3^{1/4}y^{1/2})/(zx^{1/2)}

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simplify ((3x^{-2}y^2)/(z^4))^{1/4}

simplify

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

\frac{3 ^{\frac{1}{4}} y ^{\frac{1}{2}}}{z x ^{\frac{1}{2}}}

Solution steps

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

Apply exponent rule:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

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

Simplify

(3 x^{- 2} y^{2})^{\frac{1}{4}} : \frac{3 ^{\frac{1}{4}} y ^{\frac{1}{2}}}{x ^{\frac{1}{2}}}

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

Simplify

(z^{4})^{\frac{1}{4}} : z

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

Apply the fraction rule:

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

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

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z = (\frac{1 + i}{2})^{79}

81 x^{2} + 90 x y + 25 y^{2}

- 3 x + 7 = 2 x - 18

What is ((3x^{-2}y^2)/(z^4))^{1/4} ?
The solution to ((3x^{-2}y^2)/(z^4))^{1/4} is (3^{1/4}y^{1/2})/(zx^{1/2)}