Final answer:
To write the given expression in the form of a product of three powers, we simplify each factor and combine like terms, resulting in 16a⁸b¹² × 54a¹¹b⁶ × 729a¹⁵b³.
Step-by-step explanation:
To write the given expression in the form of a product of three powers, we can simplify each factor and combine like terms. Let's break down the expression:
(2×a²×b³)⁴ = (2⁴)×(a²)⁴×(b³)⁴ = 16a⁸b¹²
2a²(3×a³×b²)³ = 2a²(3³)×(a³)³×(b²)³ = 2a²×27a⁹b⁶ = 54a¹¹b⁶
(3²×a⁵×b)³ = (3²)³×(a⁵)³×(b)³ = 729a¹⁵b³
5²×25×3²×7×3512²×18³×25⁴ = 5⁶×7×262144×5832×625 = 7320660372000
To find the final answer, we can multiply all of these simplified expressions together:
16a⁸b¹² × 54a¹¹b⁶ × 729a¹⁵b³ × 7320660372000
This is the expression written as a product of three powers.