Advanced MathHardExponents after simplifying a quotient of monomials
Advanced Math practice question
For nonzero x and y, the expression x⁻²y³ / (xy⁻¹) is equivalent to xᵃyᵇ, where a and b are constants. What is the value of a + b?
Answer: 1
Subtract exponents: x⁻² / x¹ = x⁻³ and y³ / y⁻¹ = y⁴. So a = −3, b = 4, and a + b = 1.
Common wrong answers
- If you answered 7
- 7 comes from treating both quotients as sums: |−3| + 4.
- If you answered -1
- −1 comes from y³ / y⁻¹ = y², adding the exponents' magnitudes wrongly.
- If you answered -5
- −5 comes from x⁻² · x = x⁻³ and y³ · y⁻¹ = y² with a sign slip.
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