How do you get rid of negative exponents in #(\frac { x ^ { 4} y ^ { - 2} } { x ^ { - 3} y ^ { 5} } ) ^ { - 1}#?

2 Answers
hereyougo
Mar 15, 2017

#y^7/x^7#

Explanation:

First, the -1 as the exponent of the whole fraction can simplify down to the reciprocal of the fraction itself.
#(x^-3y^5)/(x^4y^-2)#
then you can subtract the exponents in the denominator from the exponents in the numerator. This will give you
#x^-7y^7#
#x^-7=1/x^7# so
#(1/x^7)y^7#
#y^7/x^7#

EET-AP
Mar 15, 2017

#y^7/x^7#

Explanation:

Given: #((x^4y^-2)/(x^-3y^5))^-1#

The key to this one is understanding that a negative exponent means division so the result will be a reciprocal. That means to flip the numerator 'top' and denominator 'bottom'.

Since the exponent outside the bracket is #-1# we can clear it right away by flipping the whole equation to end up with a new one with exponent #1# which means multiplied by #1#:

#((x^4y^-2)/(x^-3y^5))^-1 = 1* (x^-3y^5)/(x^4y^-2)#

But #x^-3 = 1/x^3#; and #y^-2 = 1/y^2#; so:

#(x^-3y^5)/(x^4y^-2) = (y^5/x^3)/(x^4/y^2)# which we will need to invert and multiply:

#(x^-3y^5)/(x^4y^-2) = (y^5/x^3)*(y^2/x^4) = y^7/x^7#

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