How do you simplify $(2gh^4)^3[(-2g^4h)^3]^2$ ?

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Answer 1 · 2017-05-28T21:36:25

$512g^(27)h^(18)$

Start by taking the outside exponents and multiplying them through:

$(2gh^4)^(color(red)(3))[(-2g^4h)^3]^(color(red)(2))$

$=(2^(color(red)(3))g^(color(red)(3))h^(4xxcolor(red)(3)))[(-2g^4h)^(3xxcolor(red)(2))]$

Simplify

$=(8g^(3)h^12)[(-2g^4h)^(6)]$

Next, take the outside exponent of $6$ and multiply it through:

$=(8g^(3)h^12)[(-2g^4h)^(color(blue)(6))]$

$=(8g^(3)h^12)((-2)^(color(blue)(6))g^(4xxcolor(blue)(6))h^(color(blue)(6)))$

Simplify

$=(8g^(3)h^12)((-2)^(color(blue)(6))g^(4xxcolor(blue)(6))h^(color(blue)(6)))$

$=(8g^(3)h^12)(64g^(24)h^(6))$

When multiplying two identical bases with different exponents, you add the exponents over a single base.

$=8xx64g^(3)g^(24)h^(12)h^(6)$

$=512g^(3+24)h^(12+6)$

$=512g^(27)h^(18)$

How do you simplify (2gh^4)^3[(-2g^4h)^3]^2(2gh^4)^3[(-2g^4h)^3]^2?