SOLUTION: express in fractional form with positive exponents only (6x^-3 y^4)^-2

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Question 325203: express in fractional form with positive exponents only
(6x^-3 y^4)^-2
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
since x%5E%28-a%29 = 1%2Fx%5Ea, then your equation is transformed as follows:

Start with:

%286%2Ax%5E%28-3%29+%2A+y%5E4%29%5E%28-2%29

This becomes:

1+%2F+%28%286%2Ax%5E%28-3%29+%2A+y%5E4%29%5E2%29

This then becomes:


1+%2F+%28%286%2Ay%5E4%2Fx%5E3%29%5E2%29 because 6%2Ax%5E%28-3%29 is the same as 6%2Fx%5E3.

since %28a%2Fb%29%5E2 is the same as a%5E2%2Fb%5E2 then:

1+%2F+%28%286%2Ay%5E4%2Fx%5E3%29%5E2%29 becomes:

1+%2F+%28%286%2Ay%5E4%29%5E2%2F%28x%5E3%29%5E2%29%29

since 1%2F%28a%2Fb%29 is the same as %28b%2Fa%29 then:

1+%2F+%28%286%2Ay%5E4%29%5E2%2F%28x%5E3%29%5E2%29%29 becomes:

%28x%5E3%29%5E2%2F%286%2Ay%5E4%29%5E2

since %28a%5Eb%29%5Ec is the same as a%5E%28b%2Ac%29 and since %28a%2Ab%29%5Ec+=+a%5Ec%2Ab%5Ec then:

%28x%5E3%29%5E2%2F%286%2Ay%5E4%29%5E2 becomes:

%28x%5E6%29%2F%286%5E2%2Ay%5E8%29 which becomes:

%28x%5E6%29%2F%2836%2Ay%5E8%29.

If we transformed the equation correctly, then the original equation is equivalent to the final equation.

We can confirm that by taking any values for x and any values for y and seeing if both equations give us the same answer.

Let x = 4 and y = 5.

The original equation gives you a value of 000291271

The final equation gives you a value of .000291271

Since both equations give you the same answer, then the transposition can be assumed to be good.

If you really wanted to make sure, you would pick two other numbers at random and see if both equations give you the same answer.

No real reason to here so we can assume we're good.