What is (-2x^6)^4*(1/4 x)^2 ?

The solution to (-2x^6)^4*(1/4 x)^2 is x^{26}

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simplify (-2x^6)^4*(1/4 x)^2

simplify

(- 2 x^{6})^{4} \cdot (\frac{1}{4} x)^{2}

x^{26}

Solution steps

(- 2 x^{6})^{4} (\frac{1}{4} x)^{2}

Simplify

(- 2 x^{6})^{4} : 16 x^{24}

= 16 x^{24} (\frac{1}{4} x)^{2}

Simplify

(\frac{1}{4} x)^{2} : \frac{x ^{2}}{16}

= 16 x^{24} \frac{x ^{2}}{16}

Cross-cancel common factor:

16

= x^{24} x^{2}

Apply exponent rule:

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

x^{24} x^{2} = x^{24 + 2}

= x^{24 + 2}

Add the numbers:

24 + 2 = 26

= x^{26}

\frac{8}{11}

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