Final answer:
To simplify [√(63x⁵)/(y⁴)], first simplify the square root and then the denominator.
Step-by-step explanation:
To simplify the expression [√(63x⁵)/(y⁴)], we can apply the rules of exponents. First, let's break down the square root of 63x⁵ and simplify it separately.
The square root of 63 can be expressed as √(9 * 7), which simplifies to 3√7. The square root of x⁵ can be expressed as x²√x. So, the expression becomes (3√7 * x²√x) / y⁴.
Next, we can simplify the denominator by expressing it as a perfect square. The square root of y⁴ is y². So, the final simplified expression is (3√7 * x²√x) / y².