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How do you simplify #(2g^3h^-3)^2/(g^2h^0)^-3#?

Answer 1

Nathan Axel

#=(4g^12)/h^6#

Bringing the denominator to numerator as power is negative... #=(2g^3h^-3)^2×(g^2h^0)^3#

Opening the parenthesis... #=2^2g^6h^-6×g^6h^0#

As #x^0=1#, #=(4*g^6*g^6*1)/h^6#

#=(4g^12)/h^6#

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Answer 2

Jace Anderson

To simplify the expression (2g^3h^-3)^2/(g^2h^0)^-3, you follow the order of operations, which is parentheses, exponents, multiplication and division (from left to right).

First, apply the exponents: (2g^3h^-3)^2 = (2^2)(g^(32))(h^(-32)) = 4g^6h^-6 (g^2h^0)^-3 = (g^(2*-3))(h^(0*-3)) = g^-6h^0 = g^-6

Now, divide the expressions: (4g^6h^-6) / (g^-6) = 4g^(6-(-6))h^(-6-0) = 4g^12h^-6

So, the simplified expression is 4g^12h^-6.

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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.