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HELP WITH EXPONENTS











































The expression shown below contains a negative exponent.

Simplify to the maximum extent possible.

(3/AB^3)^-1

Use the general formula: x^(-a) = 1/(x^a)

Comments for HELP WITH EXPONENTS

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Sep 18, 2010
Negative Exponents
by: Staff

The question:

(3/AB^3)^-1


The answer:


An expression raised to negative exponent means:

A fraction

Numerator: 1 (always)

Denominator: the expression raised to the original exponent without the negative sign

For example: 2^-2 = 1/(2^2) = ¼, 3^-3 = 1/(3^3) = 1/27, and so forth



Apply this idea to your problem:

(3/AB^3)^-1 = 1/(3/AB^3)^1

Now simplify the expression

1/(3/AB^3)^1 = 1/(3/AB^3)

Since there are two fractions involved, multiply both the numerator and the denominator by (AB^3)/3.

(AB^3)/3 is the multiplicative inverse of the fraction in the denominator.

This will eliminate (cancel) the fraction in the denominator and give you the final simplified answer. (Sorry I had to use so many brackets.)

1/(3/AB^3) = 1 * [(AB^3)/3]/{(3/AB^3) * [(AB^3)/3]}

1 * [(AB^3)/3]/{(3/AB^3) * [(AB^3)/3]} = (AB^3)/3



The final answer is: (AB^3)/3




Thanks for writing.


Staff
www.solving-math-problems.com


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