Problem 23 - College Algebra Essentials

Question

Simplify each exponential expression. $$x^{-2} y$$

Step-by-Step Solution

Answer

The simplified form of the expression \(x^{-2} y\) is \(y / x^{2}\)

Step 1: Understanding Exponential Properties

The first concept that you need to understand is that a number raised to a negative power equals the reciprocal of that number raised to the positive power. So if we have \(x^{(-n)}\), it equals \(1/x^{n}\).

Step 2: Apply Negative Exponent Rule

We can use this rule to simplify the given expression \(x^{-2} y\). According to the rule, \(x^{-2}\) will be \(1/x^{2}\).

Step 3: Compiling the Final Result

There is no change to \(y\) as it does not have an exponent. Hence, when we write the simplified form, we get \(1/x^{2} * y\) or alternatively, it can be written as \(y / x^{2}\).