Question

Wnich expression is equivalent to the given expression? ((4xy³)/(x²))²

Answer 1

The equivalent expression for ((4xy³)/(x²))² is 16y⁶ / x², which is achieved by squaring both the numerator and the denominator and then simplifying by subtracting the exponents of the x terms.

Step-by-step explanation:

The expression you are looking to simplify is ((4xy³)/(x²))². To simplify this, we have to apply the exponent to both the numerator and the denominator. Since the exponent is outside the parentheses, everything inside the parentheses must be raised to that power. Here's how it works:

• Square the numerator: (4xy³)² = 16x²y⁶ (since (4²)(x²)(y³²) = 16x²y⁶).
• Square the denominator: (x²)² = x⁴.
• Divide the new numerator by the new denominator: 16x²y⁶ / x⁴.

Simplify the expression by subtracting the exponents in the x terms (according to the laws of exponents): 16x²y⁶ / x⁴ = 16y⁶ / x². Therefore, the simplified expression is 16y⁶ / x².