Question

For all nonzero (x) and (y), ((16x²y²)(6x²y⁻⁴)-8x²y³) equals:

a) (96x⁴y⁻² - 8x²y³)
b) (96x⁴y⁻² - 8x⁴y³)
c) (96x⁴y⁻² - 8x²y⁻¹)
d) (96x⁴y² - 8x²y⁻³)

Answer 1

The student's expression simplifies to (96x⁴y⁻² - 8x²y³), which corresponds to choice (a). The process involves multiplying coefficients and adding the exponents for variables x and y.

Step-by-step explanation:

The given expression is ((16x²y²)(6x²y⁻⁴)-8x²y³). To simplify, we first expand the multiplication part of the expression: (16x²y²) × (6x²y⁻⁴). Multiplying the coefficients gives us 16 × 6 = 96. We then add the exponents for x and y, which gives us x² × x² = x⁴ and y² × y⁻⁴ = y⁻². So the multiplication part simplifies to 96x⁴y⁻². The next part of the expression is -8x²y³ which remains unchanged. The entire expression, therefore, simplifies to (96x⁴y⁻² - 8x²y³), which matches choice (a).