Simplify ((-2u^2)/(v^4))^4

(-2u2v4)4

Move the negative in front of the fraction.

(-(2)u2v4)4

Use the power rule (ab)n=anbn to distribute the exponent.

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Apply the product rule to -2u2v4.

(-1)4(2u2v4)4

Apply the product rule to 2u2v4.

(-1)4(2u2)4(v4)4

Apply the product rule to 2u2.

(-1)424(u2)4(v4)4

Simplify the expression.

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Raise -1 to the power of 4.

124(u2)4(v4)4

Multiply 24(u2)4(v4)4 by 1.

24(u2)4(v4)4

Simplify the numerator.

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Raise 2 to the power of 4.

16(u2)4(v4)4

Multiply the exponents in (u2)4.

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Apply the power rule and multiply exponents, (am)n=amn.

16u2⋅4(v4)4

Multiply 2 by 4.

16u8(v4)4

Multiply the exponents in (v4)4.

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Apply the power rule and multiply exponents, (am)n=amn.

16u8v4⋅4

Multiply 4 by 4.

16u8v16

Simplify ((-2u^2)/(v^4))^4