SOLUTION: how can i simplify and write with positive exponents only? (b^2)^-6 over b^-4

Question 75556: how can i simplify and write with positive exponents only?
(b^2)^-6
over
b^-4
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
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First, we'll convert this to have only positive exponents, and then we'll simplify.
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Let's get the numerator to have a positive exponent. Begin by using the power rule for
exponents. This rule says that if you have a term with an exponent that is then raised
to another exponent, you multiply the two exponents. So:
.
becomes . But a base raised to a negative
number is equal to that same base to a positive number and then divided into 1. So the
numerator becomes divided by which is written as:
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Now work on the denominator. just falls under the rule to divide 1 by the
same base with a positive exponent. So the denominator becomes:
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Now putting the numerator and denominator together you get:
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Now recall that a long time ago you learned that when you divide by a fraction, you invert
the divisor and multiply the dividend by it. When you set that up, you get:
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When you multiply the numerators and denominators of both these terms you get:
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which simplifies to:
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and you perform this division by subtracting the exponent in the denominator from the
exponent in the numerator to get: . But there is a negative exponent
and the problem calls for all positive exponents. So just divide the base with a
positive exponent into 1 to get: and that is your answer.
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Hope this helps you to understand the workings of negative exponents.
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