What is (-2x^3y^2z)^3 ?

The solution to (-2x^3y^2z)^3 is -8x^9y^6z^3

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simplify (-2x^3y^2z)^3

simplify

(- 2 x^{3} y^{2} z)^{3}

- 8 x^{9} y^{6} z^{3}

Solution steps

(- 2 x^{3} y^{2} z)^{3}

Apply exponent rule:

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

n

is odd

(- 2 x^{3} y^{2} z)^{3} = - (2 x^{3} y^{2} z)^{3}

= - (2 x^{3} y^{2} z)^{3}

Apply exponent rule:

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

(2 x^{3} y^{2} z)^{3} = 2^{3} (x^{3})^{3} (y^{2})^{3} z^{3}

= - 2^{3} (x^{3})^{3} (y^{2})^{3} z^{3}

2^{3} = 8

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

Simplify

(x^{3})^{3} : x^{9}

= - 8 x^{9} (y^{2})^{3} z^{3}

Simplify

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

= - 8 x^{9} y^{6} z^{3}

\frac{x ^{- 4}}{2}

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