Question

Use the properties of exponents to rewrite the expression x²y⁵/x⁻1y⁴ in the form xᵃ*yᵇ. What are the values of a and b? Enter your answer as numbers in the order of a, b, placing a comma between the numbers, like this: 4, 2

A) a = 3, b = 1
B) a = -1, b = 1
C) a = 3, b = -1
D) a = -1, b = -1

Answer 1

The expression x²y⁵/x⁻¹y⁴ is rewritten using properties of exponents as x³y¹. When dividing similar bases, subtract the exponents in the numerator from the denominator. The values for a and b are 3 and 1, respectively, corresponding to answer choice A.

Step-by-step explanation:

To rewrite the expression x²y⁵/x⁻¹y⁴ in the form xᵃ*yᵇ, we need to use the properties of exponents. According to the properties, when dividing expressions with the same base, we subtract the exponents.

For the variable x, we subtract the exponent of the denominator from the exponent of the numerator (2 - (-1)) which equals 2 + 1, hence x³. For the variable y, we do the same (5 - 4), which equals y¹.

Therefore, the expression x²y⁵/x⁻¹y⁴ can be rewritten as x³y¹, so the values of a and b are 3 and 1, respectively.

The correct answer is A) a = 3, b = 1.