Multiplying and Dividing Rational Expressions?

Question

(4x^2 a)^2 / 12x^3 a^4. The examples in the book are easy, but I can't find the answer to this one. The question is what is the simplest form?

Also I can't get this one-- (3a^2/b)^2 X b^3/6. What is the product?
I get answers, but none of them match with the choices.

Answer 1

(4x^2a)^2 / 12x^3a^4
Square the numerator:
4^2 (x^2)^2 a^2 = 16x^4a^2

Then divide each of the like bases from the numerator and denominator.
16/12 = 4/3
x^4/x^3 = x
a^2/a^4 = 1/a^2

Put the answer back together again:
4x / 3a^2

The second problem:
Again square the numerator:
(3a^2/b)^2 = 9a^4/b^2

Then to multiply the fractions, multiply the numerators and multiply the denominators separately.
(9a^4)(b^3) = 9a^4b^3

(b^2)(6) = 6b^2

Divide top and bottom to simplify:
9a^4b^3 / 6b^2 = 3a^4b / 2

Hope this helps. Good Luck.

Answer 2

The simplest form for (4x^2 a)^2 / 12x^3 a^4 is 4x^2 / 3a^2.
The simplest form for (3a^2/b)^2 X b^3/6 is 9a^4 / b^1/2

Answer 3

I´d say it is for

a) 4x / 3a^2

b) 9a^4 / b^9/6

Answer 4

customarily, you may simplify fractions. this would propose lowering them, and it may propose changing them to complicated fractions. 15/6 could wisely be expressed as 5/2 or as 2 a million/2 i might ask your instructor how he or she expects it.

Answer 5

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