Question

(2а^2)^3*(3b)^2/(6a^3b)^2=

Answer 1

(2а^2)^3*(3b)^2/(6a^3b)^2 =  8a^6 * 9b^2 / 36a^6 * b^2 = 8 / 4 = 2.

 

Answer 2

To simplify the expression (2a^2)^3 * (3b)^2 / (6a^3b)^2, we can apply the rules of exponents and simplify each component separately. Let's break it down step by step:

First, let's simplify the numerator: (2a^2)^3 = 2^3 * (a^2)^3 = 8a^6

Now, let's simplify the denominator: (6a^3b)^2 = 6^2 * (a^3)^2 * b^2 = 36a^6b^2

Now, we can rewrite the expression: (2a^2)^3 * (3b)^2 / (6a^3b)^2 = (8a^6) * (3b)^2 / (36a^6b^2)

Next, let's simplify further: (8a^6) * (3b)^2 = 8a^6 * 9b^2 = 72a^6b^2

Now, the expression becomes: 72a^6b^2 / (36a^6b^2)

Finally, we can simplify by canceling out common factors: 72a^6b^2 / (36a^6b^2) = 2

Therefore, the simplified form of the expression (2a^2)^3 * (3b)^2 / (6a^3b)^2 is 2.