For x > 0 and y > 0, which expression is equivalent to x^-2y^3x^4y^-1?

SAT Equivalent expressions Practice Question 14 (Medium)

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Math · Advanced MathMedium

For $x > 0$ and $y > 0$ , which expression is equivalent to $\frac{x^{-2}y^3}{x^4y^{-1}}$ ?

$\frac{y^2}{x^2}$

$\frac{y^4}{x^6}$

$x^2y^2$

$\frac{y^4}{x^2}$

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Answer: B

Subtract exponents of like bases: $x^{-2 - 4} = x^{-6}$ and $y^{3 - (-1)} = y^4$ . So the expression is $x^{-6}y^4 = \frac{y^4}{x^6}$ .

Choice D adds the $x$ -exponents, $-2 + 4 = 2$ , instead of subtracting them, $-2 - 4 = -6$ .

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