How do you divide the following fraction?

((8a^5(b+1)^2/15)) / ((16a(b+1)^4/27)). The answer is (9a^4) / ((10(b+1)^2)). I know I need to multiply the first fraction by the reciprocal of the second fraction. That’s easy. However, the part that confuses me is figuring out what to do with the (b+1) exponents. Please help!

Top 1 Answers

A few days ago

Fire

Favorite Answer

Multiply the reciprocals as you said to give:

[8a^5 (b+1)^2]/15 x 27/16a (b+1)^4

Now we know that when x^(a+b) is divided by x^ (a), this is the same as x^b (e.g. 2^4 divided by 2^3 is actually 2)

So using this rule, simply cross out the (b+1)^2 and reduce the denominator to (b+1)^2

i.e.

8a^5/15 * 27/16a (b+1)^2

and then cross out the a denominator and reduce a^5 to a^4

so: 8a^4/15 * 27/16(b+1)^2

and then simplify denominators/numerators down to:

8a^4/5 * 9/16(b+1)^2

and down to:

a^4/5 * 9/2(b+1)^2

which thus gives you the answer of:

9a^4/10(b+1)^2

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