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!


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.


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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