Assuming that p neq 0 and q neq 0, simplify (pq^2)^3*(4pq^2)^(-3)*(2pq)^2*(2p^2*q^3)^2
To simplify this expression, we can use the properties of exponents, including the power rule, product rule, and quotient rule.
First, we can simplify the terms inside the parentheses:
(pq^2)^3 = p^3 * q^(2*3) = p^3 * q^6
(4pq^2)^(-3) = (4^(-3)) * (p^(-3)) * (q^(2*(-3))) = (1/64) * (1/p^3) * (1/q^6) = 1/(64p^3q^6)
(2pq)^2 = 2^2 * p^2 * q^2 = 4p^2q^2
(2p^2*q^3)^2 = 2^2 * p^(2*2) * q^(3*2) = 4p^4q^6
Next, we can substitute these simplified expressions back into the original expression and simplify further:
(pq^2)^3 * (4pq^2)^(-3) * (2pq)^2 * (2p^2*q^3)^2
= (p^3*q^6) * (1/(64p^3q^6)) * (4p^2q^2) * (4p^4q^6)
= (p^3*q^6) * (4p^2q^2) * (4p^4q^6) * (1/(64p^3q^6))
= (16p^9*q^14) / (64p^3*q^6)
= 1/4 * p^6 * q^8
Therefore, the simplified expression is 1/4 * p^6 * q^8.
