Rewrite expression to remove perfect square factors other than 1 in radicand.
√9x⁹.√18x³

The correct answer is: The given expression can be written as 9√2 x6 after removing all perfect square factors other than 1

Step-by-step solution:-
Given expression = √9x⁹ . √18x³
∴ Given expression = √[9(x)⁹ . 18(x)³] …............................................... [Product property- √m × √n = √(mn)]
∴ Given expression = √(3 × 3 × 3 × 3 × 2 × x⁹ × x³) ….......................... (Factorizing the term inside the radical)
∴ Given expression = √(3 × 3 × 3 × 3 × 2 × x⁹⁺³) .................................. [Product property- aⁿ × a^m = a^n+m]
∴ Given expression = √(3 × 3 × 3 × 3 × 2 × x¹²)
∴ Given expression = √(3 × 3) × √(3 × 3) × √2 × √x^6 × 2 …...................... [Product property- √m × √n = √(mn)]
∴ Given expression = √(3 × 3) × √(3 × 3) × √2 × √(x⁶)² ....................... [Power rule- (bⁿ)^m = b^nm]
∴ Given expression = √(3)² × √(3)² × √2 × √(x⁶)²
∴ Given expression = (3)^2/2× (3)^2/2 × √2 × (x⁶)^2/2 ............................ [Power rule- ^m√(bⁿ) = b ^n/m]
∴ Given expression = (3)¹ ×(3)¹ × √2 × (x⁶)¹
∴ Given expression = 3 × 3 × √2 × x⁶
∴ Given expression = 9√2 × x⁶

Final Answer:-
∴ The given expression can be written as 9√2 × x⁶ after removing all perfect square factors other than 1.