Final answer:
The expression (3/4 y³) × (2/3 y⁴) simplifies to 1/2 × y⁷ by multiplying the coefficients to get 1/2 and adding the exponents of y to get y⁷, thus the correct answer is OPTION D: 1/2 × y⁷.
The correct answer is OPTION D: 1/2 × y⁷.
Step-by-step explanation:
To simplify the expression (3/4 y³) × (2/3 y⁴), we will follow certain algebraic rules for multiplying fractions and combining like terms. First, multiply the coefficients (numerical parts) and then combine the variables by adding their exponents.
Multiplying the coefficients we get:
(3/4) × (2/3) = (3×2) / (4×3) = 6/12 = 1/2
Next, when multiplying variables with the same base, you add the exponents:
y³ × y⁴ = y^(3+4) = y⁷
Combining these steps, we get the final simplified expression:
1/2 × y⁷
Therefore, the correct answer is OPTION D: 1/2 × y⁷.