SOLUTION: Rewrite using positive exponent 1 _____ x^-5

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Question 472770: Rewrite using positive exponent
1
_____
x^-5
Found 2 solutions by ewatrrr, Theo:
Answer by ewatrrr(24785) About Me  (Show Source):
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
1%2Fx%5E%28-5%29 equals x%5E5.
here's how it works.
x%5E%28-5%29+=+1%2Fx%5E5
that's based on the laws of exponents.
substituting in your original expression, then:
1%2Fx%5E%28-5%29 equals 1%2F%281%2Fx%5E5%29
this is equivalent to:
1%2F%281%2Fx%5E5%29 equals 1%2A%28x%5E5%2F1%29 which equals x%5E5.
the simple way to handle it is:
if the term with the negative exponent is in the numerator, then move it to the denominator and make the exponent positive.
if the term with the negative exponent is in the denominator, then move it to the numerator and make the exponent positive.
care must be taken to move only the term with the exponent.
example 1:
3x%5E%28-5%29 equals 3%2Fx%5E5.
the term with the negative exponent is x, not 3x.
example 2:
%283x%29%5E%28-5%29 equals 1%2F%283x%29%5E5
here the term with the negative exponent is 3x because 3x is enclosed in parentheses and the term in the parentheses is being raised to the negative power.
example 3:
3a%5E%28-5%29+%2F+%28%285b%29%5E-7%29
this becomes:
%283%2A%285b%29%5E7%29%2Fa%5E5
the 3 in the numerator is not brought down to the denominator because it is not part of the term that is being raised to the negative exponent.
the (5b) in the denominator is brought to the numerator because it is part of the term that is being raised to the negative exponent.