(x^-3/5y^1/4/y^-2/3x^5/2)^60

 

Simplify and answer with positive exponents.
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There are 3 pairs of fractions separated by a division sign. The division sign inverts the quantity that follows it, so each term between division signs alternately takes the denominator or numerator position. We can take each pair of fractions and multiply their numerators and denominators: first the contents of the brackets:

(x^-3*4*3x^5)/(5y^1*y^-2*2)=12x^2/10y^-1=6x^2y/5. Here the powers, or indices, of x and y combine by addition, while the numbers combine by multiplication, then 12/10 (=4*3/5*2) cancels down to 6/5.

This all has to be raised to the power of 60: (6/5)^60*x^120y^60=56347.51x^120y^60 (approx).

by Top Rated User (1.1m points)

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