Simplifying Rational Exponents: (256x^4y)^1/4 / (16xy^3)^3/4

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MickieMik

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Apr 6, 2008
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I don't know why these get to me but here goes the problem:
(256x^4y)^1/4 / (16xy^3) ^3/4

You are supposed to multiply the exponents right?? to get;
4xy on top right??

On bottom you would mulitply (^3/1)(^3/4) to get;

16xy^15/4 then wha??

get 2xy??

Help??? My book really doesn't show how to fo these
 
Re: Simplifying Rational Exponents

One piece at a time. Don't get all anxious and try to do to much all at once.

(16xy^3)^(3/4) = 16^(3/4) * x^(3/4) * (y^3)^(3/4)
 
Re: Simplifying Rational Exponents

No. How did you get that? Where did all the other pieces go?

(16xy^3)^(3/4) = 16^(3/4) * x^(3/4) * (y^3)^(3/4)

16^(3/4) = (2^4)^(3/4) = 2^3

x^(3/4) -- Can't do much with that.

(y^3)^(3/4) = y^(9/4)

The Numerator is similar

(256x^4y)^(1/4) = 256^(1/4) * (x^4)^(1/4) * y^(1/4)

256^(1/4) = (2^8)^(1/4) = 2^2 = 4

(x^4)^(1/4) = x

y^(1/4) = y^(1/4)

One piece at a time. Trust me on this.

Now put the numerator and demoninator back together and see what you can simplfy. Don't make me do all the work. :)
 
Re: Simplifying Rational Exponents

Hello, MickieMik!

Try to follow tkhunny's advice . . . one step at a time!

\(\displaystyle \frac{(256x^4y)^{\frac{1}{4}}}{(16xy^3)^{\frac{3}{4}}}\)
Click to expand...

\(\displaystyle \text{We have: }\;\frac{(256)^{\frac{1}{4}}\left(x^4\right)^{\frac{1}{4}}\left(y^{\frac{1}{4}}\right)} {(16)^{\frac{3}{4}}\left(x^{\frac{3}{4}}\right)\left(y^3\right)^{\frac{3}{4}}}} \;\;=\;\;\frac{4\cdot x \cdot y^{\frac{1}{4}}}{8\cdot x^{\frac{3}{4}}\cdot y^{\frac{9}{4}}} \;=\;\frac{4}{8}\cdot\frac{x^1}{x^{\frac{3}{4}}} \cdot\frac{y^{\frac{1}{4}}}{y^{\frac{9}{4}}}\)

. . . . . . \(\displaystyle =\;\frac{1}{2}\cdot \left(x^{1-\frac{3}{4}}\right) \cdot\left( y^{\frac{1}{4}-\frac{9}{4}}\right) \;\;=\;\;\frac{1}{2}\cdot\left(x^{\frac{1}{4}}\right)\cdot\left(y^{-2}\right) \;\;=\;\;\boxed{\frac{x^{\frac{1}{4}}}{2y^2}}\)

 
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