(5%5E%E2%88%9210).jpeg "(5^−8)(5^−10)")
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.