Simplify!!

54 a^2 b^3
___________
81 a^3 b^2

Choices are::

A. 2/3 a^2 b

B. 2a^2
____
3b

54 a^2 b^3

___________
81 a^3 b^2

= (54/81)(a^2/a^3)(b^3/b^2)
= (2/3) b/a or 2b/(3a)

I don't see that choice, but that is your answer.

I'm sorry but that is not a choice.

You are right, I should have had

(3/2)b/a or 3b/(2a)

Simplify!!

54 a^2 b^3
___________
81 a^3 b^2

Choices are::

A. 2a^2 b
_____
3
I have revised my choices! now try

B. 2a^2
____
3b

There can't be a^2 in your answer

just looking at the a's you had a^2/a^3 which is 1/a

once more:

54 a^2 b^3
___________
81 a^3 b^2

= (3/2) (1/a) (b)

= (3/2)b/a or 3b/(2a)

To simplify the expression, we can divide the numerator and denominator by their greatest common factor.

Let's break down each term:

54 can be factored as 2 * 3^3.
a^2 can be written as a * a.
b^3 can be written as b * b * b.

81 can be factored as 3^4.
a^3 can be written as a * a * a.
b^2 can be written as b * b.

Now let's simplify the expression:

(54 a^2 b^3) / (81 a^3 b^2)

We can cancel out common factors between the numerator and the denominator. We have two 3s in the numerator and four 3s in the denominator (from 3^3 and 3^4). Thus, we can cancel out two 3s.

After canceling out the common factors, we have:

[(2 * a * a * b * b * b) / (3 * a * a * a * b * b)]

Now, let's simplify further:

(2 * a * b * b * b) / (3 * a * a * b * b)

We can cancel out a b from both the numerator and the denominator:

(2 * b * b) / (3 * a * a)

This can be written as:

(2b^2) / (3a^2)

So, the simplified expression is (2b^2) / (3a^2).

Therefore, the correct choice is:

B. 2b^2 / 3a^2