Which expression is equivalent to (3x^2y)^3? | SAT Equivalent expressions Question, Answer Explained

Math · Advanced MathEasy

Which expression is equivalent to $(3x^2y)^3$ ?

$3x^6y^3$

$9x^6y^3$

$27x^5y^3$

$27x^6y^3$

Show answer and explanation

Answer: D

Raise each factor to the third power: $3^3 = 27$ , $(x^2)^3 = x^{2 \cdot 3} = x^6$ , and $y^3$ . So $(3x^2y)^3 = 27x^6y^3$ .

Choice B multiplies $3$ by $3$ instead of cubing it.

Why the other choices are wrong

A. This applies the exponent to x and y but not to the coefficient 3, which becomes 3³ = 27.
B. This multiplies 3 by 3. The coefficient must be cubed: 3 × 3 × 3 = 27.
C. This adds the exponents 2 and 3. A power raised to a power multiplies the exponents, giving x⁶.

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