Question

(a^-3b^2/2c)^2•(2c)^3•a^6/b^5

Answer 1

………=(b^4/a^6*4c^2) *8c^3 *(a^6/b^5)=(8a^6 b^4 c^3) / (4a^6 b^5c^2)=2c/b

Answer 2

Let's simplify the expression step by step:

First, let's simplify the term within the parentheses: (a^-3b^2/2c)^2 = a^-6b^4/4c^2

Next, let's simplify the term (2c)^3: (2c)^3 = 8c^3

Now, let's substitute these simplified terms back into the expression: (a^-3b^2/2c)^2 • (2c)^3 • a^6/b^5 = (a^-6b^4/4c^2) • (8c^3) • a^6/b^5

Next, let's simplify the expression further by combining like terms in the numerator and denominator:

In the numerator, we have: (a^-6b^4 • a^6) = a^-6+6 • b^4 = a^0 • b^4 = b^4

In the denominator, we have: (4c^2 • b^5) = 4 • c^2 • b^5

Substituting these simplified terms back into the expression, we have: (b^4) / (4 • c^2 • b^5)

Now, let's simplify the expression further by canceling out common factors:

We can cancel out one of the b's in the numerator and denominator, resulting in: 1 / (4 • c^2 • b)

So, the simplified expression is: 1 / (4 • c^2 • b)