Essence Byrd

2022-04-28

Simplify with fractional exponents and negative exponents

I am trying to simplify

$\left(\frac{3{x}^{\frac{3}{2}}{y}^{3}}{{x}^{2}{y}^{-\frac{1}{2}}}\right)}^{-2$

It seems pretty simple at first. I know that a negative exponent means you flip a fraction. So I flip it.

$\left(\frac{{x}^{2}{y}^{-\frac{1}{2}}}{3{x}^{\frac{3}{2}}{y}^{3}}\right)}^{2$

Now I need to square it, which is tricky because there are a lot of weird rules with squaring. This is probably where I went wrong.

$\left(\frac{{x}^{2}{y}^{-\frac{1}{2}}}{9{x}^{\frac{3}{2}}{y}^{3}}\right)$

Now I need to try and simplify things. I know that I can get rid of the x on top since there is a larger one on the bottom.

$\frac{4}{2}-\frac{3}{2}=\frac{1}{2}$

$\left(\frac{{x}^{\frac{1}{2}}{y}^{-\frac{1}{2}}}{9{y}^{3}}\right)$

Now I need to get rid of the y exponent.

I am not sure how that is possible.

I am trying to simplify

It seems pretty simple at first. I know that a negative exponent means you flip a fraction. So I flip it.

Now I need to square it, which is tricky because there are a lot of weird rules with squaring. This is probably where I went wrong.

Now I need to try and simplify things. I know that I can get rid of the x on top since there is a larger one on the bottom.

Now I need to get rid of the y exponent.

I am not sure how that is possible.

4dorts3x

Beginner2022-04-29Added 9 answers

So we have

$\left(\frac{3{x}^{\frac{3}{2}}{y}^{3}}{{x}^{2}{y}^{-\frac{1}{2}}}\right)}^{-2$

Yes you are right you can "flip" the fraction to remove the negative exponent.

$\left(\frac{{x}^{2}{y}^{-\frac{1}{2}}}{3{x}^{\frac{3}{2}}{y}^{3}}\right)}^{2$

Here you multiply every exponent by 2 to square the expression inside the brackets. This is where you went wrong here.

$\left(\frac{{x}^{4}{y}^{-1}}{9{x}^{3}{y}^{6}}\right)$

But$y}^{-1}=\frac{1}{y$

so the above is equal to

$\left(\frac{{x}^{4}}{9{x}^{3}{y}^{7}}\right)$

Now cancel the$x}^{3$

$\left(\frac{x}{9{y}^{7}}\right)$

And we're done.

Yes you are right you can "flip" the fraction to remove the negative exponent.

Here you multiply every exponent by 2 to square the expression inside the brackets. This is where you went wrong here.

But

so the above is equal to

Now cancel the

And we're done.

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