So I had a question on Algebra II homework.

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5t^3/4s divided by 16s^2/25t^3 multiplied by 16s/25t^3.

If you could, I would like a step by step elaboration.

Jul 23rd, 2015

Thank you for the opportunity to help you with your question!

((5t^3/4s)/(16s^2/25t^3))*(16s/25t^3)

In order to perform the division we just need to multiply the fraction of the top by the flipped fraction of the bottom like this:

((5t^3/4s)/(16s^2/25t^3))*(16s/25t^3) = (5t^3/4s)*(25t^3/16s^2)*(16s/25t^3)

Then let's notice that we can cancel out somethings.

(5t^3/4s)*(25t^3/16s^2)*(16s/25t^3)

The 16's and the 25t^3's would cancel out, so then we would have the following:

= (5t^3/4s)*(1/s^2)*(s)

After this, we multiply all what we have on the top over the multiplication of all the expressions of the bottom.

(5t^3/4s)*(1/s^2)*(s)  = (5t^3 * 1 * s)/(4s * s^2) = 5t^3s/(4s*s^3)

Then let's notice that the s's can cancel out.

5t^3s/(4s*s^3) = 5t^3/4s^3

Since the t and s are raised to the power 3 then we can rewrite it like t over s all raised to the power 3 like this.

5t^3/4s^3 = 5/4(t/s)^3

So we can write 5t^3/4s^3 or 5/4(t/s)^3.

Final asnwer:  5t^3/4s^3  or    5/4(t/s)^3

Please let me know if you need any clarification. I'm always happy to answer your questions.
Jul 23rd, 2015

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