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

Answer 1

Hazel Anglin

#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)#

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Answer 2

Abigail Allen

To simplify the expression, follow these steps:

Simplify the expressions within the parentheses and brackets.
Apply the exponent laws to simplify each expression.
Combine like terms, if possible.

The simplified expression is: -64g^15h^18.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.