You can put this solution on YOUR website! Please help me simplify using the rules of exponents!
#26 Change the outermost negative exponent (-3) to a positive value by putting the expression down in the denominator, thus: Now change the negative exponent of x (-1) to a positive vlue by putting up in the numerator, thus: Finally, multiply the exponent of every factor inside the parentheses by the outermost expont (3).
#38 Here you can change the outermost negative exponent (-3) to a positive value simply by inverting the expression, thus: Finally, multiply the exponent of evey factor inside the parentheses by the outermost exponent (3). or
You can put this solution on YOUR website!
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The rules are that when you raise an algebraic expression to a power (in this problem that
power is -3) you raise each factor in the expression by that power, and if that factor already
has an exponent, you multiply that exponent by the power. Sound confusing? Let's try to straighten
things out.
In this problem you have 3 factors: the 2, the , and the . We need to raise
each of these factors to the -3 power. For the 2 we get . Next for the when
we raise it to the -3 power we multiply -1 by -3 and get a new exponent of +3. So in raising we get an answer of . Finally, the factor . In raising this
to the -3 power we multiply the exponents . So the result is .
Putting all three of these factors together results in:
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Then according to the rules of negative exponents, a term raised to a negative exponent will
be the same as the dividing that term with a positive exponent into 1. This means that is the same as 1 divided by . So . And , of course, so .
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Similarly, . Introducing these changes for negative exponents now
makes the final answer:
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That's the answer to the first problem. On to the second problem ...
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If we replace the x that is in the denominator by in the numerator the problem becomes:
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This has lots of similarity with the first problem above. So without a lot of explanation:
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and
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and finally:
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Putting this string of factors together results in an answer of:
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Hope that you can follow this and see how the several rules of exponents that were applied
combine to give you an answer.
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