Working with Fractional Powers

**cmf0106** · May 23rd 2008, 10:20 AM

Not sure how to solve the last part of this problem. The original equation reads:

$\sqrt{xy^3} (\sqrt{x^5y} - \sqrt{xy^7})$

So then you raise the powers to get some nicer exponents to work which looks like this

$x^\frac{1}{2}y^\frac{3}{2}(x^\frac{5}{2}y^\frac{1} {2}) - x^\frac{1}{2}y^\frac{3}{2}(x^\frac{1}{2}y^\frac{7} {2})$

and here is where I am lost, the author adds the exponents of the variables and ends up with

$x^\frac{6}{2}y^\frac{4}{2}-x^\frac{2}{2}y^\frac{10}{2}$

How is the author getting x^6/2, y^4/2 when you distribute for the first part of the equation? I am completely clueless as to how she did this could someone please fill me in. Thanks!

**colby2152** · May 23rd 2008, 10:37 AM

Originally Posted by cmf0106

Not sure how to solve the last part of this problem. The original equation reads:

$\sqrt{xy^3} (\sqrt{x^5y} - \sqrt{xy^7})$

So then you raise the powers to get some nicer exponents to work which looks like this

$x^\frac{1}{2}y^\frac{3}{2}(x^\frac{5}{2}y^\frac{1} {2}) - x^\frac{1}{2}y^\frac{3}{2}(x^\frac{1}{2}y^\frac{7} {2})$

and here is where I am lost, the author adds the exponents of the variables and ends up with

$x^\frac{6}{2}y^\frac{4}{2}-x^\frac{2}{2}y^\frac{10}{2}$

How is the author getting x^6/2, y^4/2 when you distribute for the first part of the equation? I am completely clueless as to how she did this could someone please fill me in. Thanks!

The 1st term looks like this:

$x^\frac{1}{2}y^\frac{3}{2}(x^\frac{5}{2}y^\frac{1} {2})$

To find the new exponent of x, add the two different exponents because this property holds:

$x^a * x^b = x^{a+b}$

Therefore: $\frac{1}{2}+\frac{5}{2}=3$ , and the new exponent for x is 3. Likewise, y now has an exponent of 2.

**Moo** · May 23rd 2008, 10:41 AM

Hello,

Originally Posted by cmf0106

Not sure how to solve the last part of this problem. The original equation reads:

$\sqrt{xy^3} (\sqrt{x^5y} - \sqrt{xy^7})$

So then you raise the powers to get some nicer exponents to work which looks like this

$x^\frac{1}{2}y^\frac{3}{2}(x^\frac{5}{2}y^\frac{1} {2}) - x^\frac{1}{2}y^\frac{3}{2}(x^\frac{1}{2}y^\frac{7} {2})$

and here is where I am lost, the author adds the exponents of the variables and ends up with

$x^\frac{6}{2}y^\frac{4}{2}-x^\frac{2}{2}y^\frac{10}{2}$

How is the author getting x^6/2, y^4/2 when you distribute for the first part of the equation? I am completely clueless as to how she did this could someone please fill me in. Thanks!

The rule states : $a^b a^c=a^{b+c}$

$x^{\frac 12}y^{\frac 32}(x^{\frac 52}y^{\frac 12})=x^{\frac 12}y^{\frac 32}x^{\frac 52}y^{\frac 12}=x^{\frac 12}x^{\frac 52}y^{\frac 32}y^{\frac 12}=\dots$

**cmf0106** · May 23rd 2008, 10:52 AM

Thanks for the input everyone! I just realized I made a mistake. At times I forgot the author assumes that one is not utilizing a calculator.

1/2+5/2 she had 6/2

I just punched it in the calculator and got 3 and skipped one of her steps. Very stupid of me for not seeing this earlier, thanks!

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