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5 votes
PLEASE HELP

Evaluate 3x^3y-2/5x^-2y^3 for x=2 and y=3

32/405
160/81
2/5

User Adrianus
by
4.7k points

1 Answer

5 votes

Let's try to simplify that a bit. Rewriting it in its current form it looks like this:


(3x^3y^(-2))/(5x^(-2)y^3).

We could split it up and deal with one problem at a time if we do this:


(3)/(5)*(x^3)/(x^(-2))*(y^(-2))/(y^3).

The rule with like bases and division of the exponents is that we subtract the lower exponent from the upper so that would be


x^(3-(-2))*y^(-2-3)

which gives us new exponents of


x^5*y^(-5).

We rewrite to make that negative exponent a positive by putting it under a 1, so the whole problem with no negatives looks like this now:


(3x^5)/(5y^5).

If x = 2 and y = 3, we sub in accordingly:


(3(2)^5)/(5(3)^5) =(3(32))/(5(243))

which simplifies to
(96)/(1215)=(32)/(405), the first choice above.

User Angelo Giuffredi
by
5.1k points
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