SOLUTION: Simplify the eepression: (8x^6y^9)^(2/3)/(16x^8y^-4)^(1/2) I don't know weather to work this like a polynomial and divide. My problem just seems to get longer than shorter. Thank

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Simplify the eepression: (8x^6y^9)^(2/3)/(16x^8y^-4)^(1/2) I don't know weather to work this like a polynomial and divide. My problem just seems to get longer than shorter. Thank       Log On


   

Question 510537: Simplify the eepression: (8x^6y^9)^(2/3)/(16x^8y^-4)^(1/2)
I don't know weather to work this like a polynomial and divide. My problem just seems to get longer than shorter. Thank you so much for your help.
(I gave you the wrong email address the first time. Sorry
Answer by bucky(2189) About Me  (Show Source):
You can put this solution on YOUR website!
Given to simplify:
.
%288x%5E6y%5E9%29%5E%282%2F3%29%2F%2816x%5E8y%5E-4%29%5E%281%2F2%29
.
In the numerator replace 8 by its equivalent 2%5E3 and in the denominator replace 16 by its equivalent 2%5E4. You then have:
.
%282%5E3x%5E6y%5E9%29%5E%282%2F3%29%2F%282%5E4x%5E8y%5E-4%29%5E%281%2F2%29
.
Now use the power rule in both the numerator and the denominator. The power rule tells you that you multiply the exponents of each factor in the quantity by the exponent to which the quantity is being raised. So in the numerator multiply the exponent 2%2F3 times each of the factor exponents (times 3 for the base 2, times 6 for the base x, and times 9 for the base y). Do the same for the denominator, that is multiply the exponent 1%2F2 times each of the factor exponents (times 4 for the base 2, times 8 for the base x, and times -4 for the base y). When you do this you should have:
.

.
Note that the rendering may be a little too large to display the above step clearly, especially for the exponents in the numerator. They may be "clipped off" slightly. If that is the case, just look at what is done in the denominator and you should get the general idea. The same thing was done in the numerator where each exponent is multiplied by 2%2F3. (The horizontal bar that shows might appear to cross out exponents in the denominator. It does not. Just imagine it raised so that it is the dividing line between the numerator and denominator.)
.
Then multiply the exponents and you get:
.
2%5E2x%5E4y%5E6%2F2%5E2x%5E4y%5E%28-2%29
.
Note that the 2%5E2 in the numerator cancels with the same term in the denominator. Then note that the x%5E4 in the numerator cancels with the same term in the denominator. What you are left with is:
.
y%5E6%2Fy%5E%28-2%29
.
When you do this division the rule is that for dividing terms of a common base, subtract the exponent of the denominator from the exponent in the numerator.
.
So this becomes:
.
y%5E%286+-%28-2%29%29
.
And this becomes:
.
y%5E%286%2B2%29
.
This gives you the answer of:
.
y%5E8
.
Hope this helps simplify things for you.