What is (-2v^7)^3(-4v^2)^4 ?

The solution to (-2v^7)^3(-4v^2)^4 is -2048v^{29}

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simplify (-2v^7)^3(-4v^2)^4

simplify

(- 2 v^{7})^{3} (- 4 v^{2})^{4}

- 2048 v^{29}

Solution steps

(- 2 v^{7})^{3} (- 4 v^{2})^{4}

Simplify

(- 2 v^{7})^{3} : - 8 v^{21}

= - 8 v^{21} (- 4 v^{2})^{4}

Simplify

(- 4 v^{2})^{4} : 256 v^{8}

= - 8 v^{21} \cdot 256 v^{8}

Multiply the numbers:

- 8 \cdot 256 = - 2048

= - 2048 v^{21} v^{8}

Apply exponent rule:

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

v^{21} v^{8} = v^{21 + 8}

= - 2048 v^{21 + 8}

Add the numbers:

21 + 8 = 29

= - 2048 v^{29}

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