Question

Select the correct answer.

Which expression is equivalent to 40x^2√x^12 / 10x^2√29x^8, if x ≠ 0?


A. 4x^2√29/√29


B. 30x^2√29/29


C. 4x^2√29


D. 4x^2√29/29

Answer 1

To simplify the expression 40x²√x¹² / 10x²√29x⁸, divide the numerical coefficients, divide the variables with exponents, and subtract the exponents of the square roots. The simplified expression is 4x^2√(1 / 29), and the correct answer is option A: 4x²√29/√29.

Step-by-step explanation:

To simplify the expression 40x²√x¹² / 10x²√29x⁸:

1. Divide the numerical coefficients: 40/10 = 4
2. Divide the variables with exponents: x² / x² = 1
3. Subtract the exponents of the square roots: √x¹² / √29x⁸ = √(x¹² / 29x⁸) = √(x⁴ / 29) = x²√(1 / 29)

Combining all the simplifications, the expression is equivalent to 4x²√(1 / 29). Therefore, the correct answer is option A: 4x²√29/√29.