(-5g^5h^6)^2(g^4h^2)^4
-5^2 = +25
so
25 g^10 h^12 g^16 h^8
= 25 g^26 h^20
To simplify the given expression, we can use the rules of exponents. Let's break it down step by step:
Step 1: Apply the exponent to each term inside the parentheses:
(-5g^5h^6)^2 = (-5)^2(g^5)^2(h^6)^2 = 25g^10h^12
(g^4h^2)^4 = (g^4)^4(h^2)^4 = g^16h^8
Step 2: Multiply the two simplified expressions:
25g^10h^12 * g^16h^8
To multiply when the bases are the same, we add the exponents:
25 * g^(10 + 16) * h^(12 + 8)
Simplifying the exponents:
25 * g^26 * h^20
So the simplified expression is 25g^26h^20.