Question

(2p^3)^3*5(pq^5)^2*2q

Answer 1

(2p^3)^3*5(pq^5)^2*2q=8p^9*5p^5*5q^10*2q=40p^14*10q^11

Answer 2

To simplify the expression, we'll apply the rules of exponents and combine like terms. Let's break it down step by step:

Step 1: Simplify each term within the parentheses using the exponent rule (a^m)^n = a^(m * n):

1. (2p^3)^3 = 2^3 * (p^3)^3 = 8 * p^(3 * 3) = 8 * p^9
2. (pq^5)^2 = (p^1 * q^5)^2 = p^(1 * 2) * q^(5 * 2) = p^2 * q^10

Step 2: Multiply all the simplified terms:

(2p^3)^3 * 5 * (pq^5)^2 * 2q = (8 * p^9) * 5 * (p^2 * q^10) * 2q

Step 3: Combine like terms:

= 8 * 5 * 2 * p^9 * p^2 * q^10 * q

Step 4: Perform the multiplications:

= 80 * p^(9 + 2) * q^(10 + 1)

Step 5: Simplify the exponents:

= 80 * p^11 * q^11

So, the simplified expression is:

80p^11q^11