Question

Simplify. Write your final answer without using negative exponents: (x^(10)y^(-11))(x^(-15)y^(9))

Answer 1

`\[ (x^(-5)y^(-2))/(x^5y^(20)) \]`

To simplify the given expression, subtract the exponents of (x) and (y) in each term. This results in
`\(x^(-5)y^(-2)\)` in the numerator and
`\(x^5y^(20)\)` in the denominator.

This simplifies further to
`\((1)/(x^5y^2)\)` since negative exponents indicate reciprocals.

Step-by-step explanation:

The given expression
`(x^(10)y^(-11))(x^(-15)y^9)` involves multiplying two terms with different bases, (x) and (y), and different exponents. To simplify, we apply the rules of exponents. When multiplying terms with the same base, you add their exponents. In this case, for (x), (10 + (-15) = -5), and for (y), (-11) + 9 = -2. This gives us
`\(x^(-5)y^(-2)\)`.

To express the result without negative exponents, we move the terms with negative exponents to the denominator, resulting in
`\((1)/(x^5y^2)\)`. This is the final simplified form of the given expression.

Understanding and manipulating expressions with exponents is fundamental in algebra. It's crucial to grasp the rules governing exponents, such as how to combine terms with the same base and handling negative exponents. This knowledge is applicable in various mathematical contexts, providing a foundation for solving equations and simplifying complex expressions.