What is (-4x^6y)(2x^{-2}y^5)^3 ?

The solution to (-4x^6y)(2x^{-2}y^5)^3 is -32y^{16}

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simplify (-4x^6y)(2x^{-2}y^5)^3

simplify

(- 4 x^{6} y) (2 x^{- 2} y^{5})^{3}

- 32 y^{16}

Solution steps

(- 4 x^{6} y) (2 x^{- 2} y^{5})^{3}

Apply rule:

(- a) = - a

(- 4 x^{6} y) = - 4 x^{6} y

= - 4 x^{6} y (2 x^{- 2} y^{5})^{3}

Simplify

(2 x^{- 2} y^{5})^{3} : \frac{8 y ^{15}}{x ^{6}}

= - 4 x^{6} y \frac{8 y ^{15}}{x ^{6}}

Cross-cancel common factor:

x^{6}

= - 4 y \cdot 8 y^{15}

Multiply the numbers:

- 4 \cdot 8 = - 32

= - 32 y y^{15}

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

y y^{15} = y^{1 + 15}

= - 32 y^{1 + 15}

Add the numbers:

1 + 15 = 16

= - 32 y^{16}

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

a^{2} \cdot b^{- 8}

(x - 4) 2 - 16

24 x^{2} - 43 x y + 18 y^{2}

(3 e^{- x})^{2}

What is (-4x^6y)(2x^{-2}y^5)^3 ?
The solution to (-4x^6y)(2x^{-2}y^5)^3 is -32y^{16}