What is an equivalent expression for 5√4x¹⁷.

The correct answer is: ∴ 10x8 × √x is an equivalent of the given expression 5√4x17

Step-by-step solution:-
Given expression = 5√4x¹⁷
∴ Given expression = 5 × √(2 × 2 × x⁸⁺⁸⁺¹) ….................................... (Factorizing the given expression)
∴ Given expression = 5 × √(2 × 2 × x⁸ × x⁸ × x) ....................................... [aⁿ ⋅ a^m = a^n+m]
∴ Given expression = 5 × √(2 × 2) × √(x⁸ × x⁸) × √x ….......................... [Product property - √m × √n = √(mn)]
∴ Given expression = 5 × √(2)² × √(x⁸)² × √x
∴ Given expression = 5 × (2)^2/2 × (x⁸)^2/2 × √x .................................... [Power rule- ^m√(bⁿ) = b ^n/m]
∴ Given expression = 5 × (2)¹ × (x⁸)¹ × √x
∴ Given expression = 5 × 2 × x⁸ × √x
∴ Given expression = 10x⁸ × √x
Final Answer:-
∴ 10x⁸ × √x is an equivalent of the given expression 5√4x¹⁷.