Question

What is the sum of all exponents when ((x^4y^2)(x^3y)^3)/((x^3y^2)(x^2y)) is written in simplest form with all exponents non-negative.

Answer 1

The sum of all exponents when
`\(\frac{{(x^4y^2)(x^3y)^3}}{{(x^3y^2)(x^2y)}}\)` is written in simplest form with all exponents non-negative is 12.

Step-by-step explanation:

To simplify the expression, let's perform the operations step by step.
`\(\frac{{(x^4y^2)(x^3y)^3}}{{(x^3y^2)(x^2y)}}\)` can be rewritten as
`\(\frac{{x^4y^2x^9y^3}}{{x^3y^2x^2y}}\)`. Simplifying the terms within the numerator and the denominator gives
`\(\frac{{x^(13)y^5}}{{x^5y^3}}\)`. To further simplify, we subtract the exponents in the denominator from the exponents in the numerator:
`\(x^(13-5)y^(5-3)\)`, resulting in
`\(x^8y^2\).`

The sum of all exponents in the simplified form
`\(x^8y^2\)` is 8+2 = 10. Therefore, the sum of all exponents when the given expression is written in simplest form with all exponents non-negative is 10. Apologies for the mistake in the initial calculation.

Therefore, after simplifying the given expression to
`\(x^8y^2\)`, the sum of all exponents is 8+2 = 10, not 12.