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

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

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Answer 1 · 2017-05-28T21:36:25

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

Explanation:

Start by taking the outside exponents and multiplying them through:

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

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

Simplify

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

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

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

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

Simplify

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

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

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

$= 8 \times 64 g^{3} g^{24} h^{12} h^{6}$ $=8xx64g^(3)g^(24)h^(12)h^(6)$

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

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

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

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