Question

Simplify. {4x^{-3}y^2}/{8x^5y^{-4}}

a. {2y^4}/{x^7}
b. {2x^4}/{y^7}
c. {y^6}/{2x^8}
d. {y^5}/{2x^6}

Answer 1

The expression {4x^{-3}y^{2}}/{8x^{5}y^{-4}} simplifies to {y^{6}}/{2x^{8}} after dividing coefficients and using exponent rules to combine like terms, which matches answer option c.

Step-by-step explanation:

The student is asking to simplify the expression {4x-3y2}/{8x5y-4}. To solve this, we will use the properties of exponents.

First, divide the coefficients: 4/8 simplifies to 1/2.

Next, subtract the exponents of x: -3 - 5 becomes -8, so x-8 moves to the denominator and becomes x8.

Then subtract the exponents of y: 2 - (-4) becomes 6, so y6 remains in the numerator.

The simplified expression is {y6}/ {2x8}, which matches answer option c.