## Simplifying Exponential Expressions: (5^−8)(5^−10)

This article will guide you through simplifying the expression (5^−8)(5^−10). We'll break down the steps and explain the rules of exponents that are involved.

### Understanding Exponents

An exponent indicates how many times a base number is multiplied by itself. For example, 5^3 means 5 * 5 * 5.

### Rule of Exponents: Multiplication

When multiplying exponents with the same base, we add the powers together. This rule can be expressed as:

**x^m * x^n = x^(m+n)**

### Applying the Rule

Let's apply this rule to our expression: (5^−8)(5^−10)

**Identify the base:**The base in this expression is 5.**Add the exponents:**-8 + (-10) = -18**Combine the results:**(5^−8)(5^−10) = 5^(-18)

### Simplifying Negative Exponents

A negative exponent indicates that the base is in the denominator of a fraction. This rule can be expressed as:

**x^-n = 1/x^n**

Applying this to our expression:

5^(-18) = 1/5^18

### Final Result

Therefore, the simplified expression of (5^−8)(5^−10) is **1/5^18**.