Simplify the Square Root Expression: √(64x²/x⁴)

Solve the following exercise:

$\sqrt{\frac{64x^2}{x^4}}=$

To solve this problem, we'll simplify the expression inside the square root step-by-step:

• Step 1: Simplify the fraction $\frac{64x^2}{x^4}$ using the quotient rule for exponents:
• $\frac{64x^2}{x^4} = 64 \cdot x^{2-4} = 64 \cdot x^{-2}$.
• Step 2: Now apply the square root to the simplified expression:
• $\sqrt{\frac{64x^2}{x^4}} = \sqrt{64x^{-2}} = \sqrt{64} \cdot \sqrt{x^{-2}}$.
• $\sqrt{64} = 8$ and $\sqrt{x^{-2}} = x^{-1}$ (since it represents inverse squaring).
• Thus, $\sqrt{64x^{-2}} = 8 \cdot x^{-1} = \frac{8}{x}$.

Therefore, the solution to the problem is $\frac{8}{x}$, which matches choice 1.