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How do you simplify #(100^(1/2))^-4#?

Answer 1

Kennedy Adams

See full simplification process below

First step is to simplify the terms in the parenthesis:

#(100^(1/2))^-4 = 10^-4#

Next we can use this rule for exponents to further simplify:

#x^color(red)(a) = 1/x^color(red)(-a)#

Substituting gives:

#10^color(red)(-4) = 1/10^color(red)(- -4) = 1/10^4 = 1/(10 xx 10 xx 10 xx 10) =#

#1/10000# or #0.0001#

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Answer 2

Eva Abramson

To simplify ( (100^{\frac{1}{2}})^{-4} ), you apply the exponent rule which states that ( (a^m)^n = a^{m \times n} ). So, ( (100^{\frac{1}{2}})^{-4} = 100^{\frac{1}{2} \times -4} = 100^{-2} ). Finally, ( 100^{-2} = \frac{1}{100^2} = \frac{1}{10000} ).

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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.