What is (2xy^{-2}*2y^2)^3 ?

The solution to (2xy^{-2}*2y^2)^3 is 64x^3

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simplify (2xy^{-2}*2y^2)^3

simplify

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

64 x^{3}

Solution steps

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

Apply exponent rule:

(a \cdot b)^{n} = a^{n} b^{n}

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

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

2^{3} = 8

= 8 x^{3} (y^{- 2})^{3} \cdot 2^{3} (y^{2})^{3}

Simplify

(y^{- 2})^{3} : \frac{1}{y ^{6}}

= 8 x^{3} \frac{1}{y ^{6}} \cdot 2^{3} (y^{2})^{3}

2^{3} = 8

= 8 x^{3} \frac{1}{y ^{6}} \cdot 8 (y^{2})^{3}

Simplify

(y^{2})^{3} : y^{6}

= 8 x^{3} \frac{1}{y ^{6}} \cdot 8 y^{6}

Simplify

8 x^{3} \frac{1}{y ^{6}} \cdot 8 y^{6} : 64 x^{3}

= 64 x^{3}

- x 90 x^{5} - x^{2} 10 x^{3}

(- 2 + 2 i) \cdot (5 + 5 i)

8 + x^{6}

218 + 8 + 43

\frac{x ^{2} + x - 6}{2 x + 6}