Question

Simplify and explain:
(3b^3c^2)^2 times (2ab^2c^0)^3

Answer 1

To simplify the expression (3b^3c^2)^2 times (2ab^2c^0)^3, we need to apply the rules of exponentiation. First, we raise each base to the power of the exponent outside the parentheses. Then, we simplify each term and multiply the resulting terms together.

Step-by-step explanation:

To simplify the expression (3b3c2)2 times (2ab2c0)3, we need to apply the rules of exponentiation. First, we raise each base to the power of the exponent outside the parentheses:

(3b3c2)2 = 32 * (b3)2 * (c2)2

Then, simplify each term:

32 = 9

(b3)2 = b6

(c2)2 = c4

Next, we raise each base to the power of the exponent outside the parentheses:

(2ab2c0)3 = 23 * (a3)3 * (b2)3 * (c0)3

Again, simplify each term:

23 = 8

(a3)3 = a9

(b2)3 = b6

(c0)3 = c0 = 1

Finally, multiply the resulting terms together:

9 * b6 * c4 * 8 * a9 * b6 * 1 = 72a9b12c4