Could someone PLEASE explain to me why my answer to this problem is incorrect? It must be a reduction issue but I'm totally missing it. Find the square root of 16x to the third power over x to the fifth power.... My answer is 4 square root of x over x to the fourth power. H E L P !!!

\[\sqrt{\frac{16x ^{3}}{x ^{5}}}=4\sqrt{\frac{x ^{3}}{x ^{5}}}=4\sqrt{\frac{1}{x ^{2}}}\] Can you finish it now?

Tell me if I'm on the right track...since the x in the denominator is still squared, can't I pull it out and put it with the "4" so that the answer would read 4x square root of 1? |dw:1363111076559:dw|

\[4\sqrt{\frac{1}{x ^{2}}}=4\sqrt{(\frac{1}{x}}\times \frac{1}{x})=?\]

Can you find this one? \[\sqrt{a ^{2}}=?\]

My answer is not correct.

how about 4/x. is that it?

How did you get the answer 4/x ?

I think I pulled the square out of the radican, then replaced it with the parenthesis so that it read 4(1/x), multiplied that out by removing the parenthesis and got 4/x for the answer. is that the correct way to go?

Good work! Yes the correct answer is 4/x.

What I don't understand in your first post is how come whe x to the second power over x to the fifth power turned into 1/x to the second power. Can you please explain that to me?

\[\frac{1}{x ^{5}}=x ^{-5}\] \[\frac{x ^{3}}{x ^{5}}=x ^{3}\times x ^{-5}=x ^{-2}=\frac{1}{x ^{2}}\] Another way to look at it is as follows: \[\frac{x ^{3}}{x ^{5}}\] Divide the numerator and the denominator by x^3 \[\frac{\frac{x ^{3}}{x ^{3}}}{\frac{x ^{5}}{x ^{3}}}=\frac{1}{x ^{2}}\]

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