Evaluate each exponential expression: 5^-3• 5

Verified step by step guidance

1. Recall the property of exponents that states when multiplying powers with the same base, you add the exponents: \(a^m \cdot a^n = a^{m+n}\).
2. Identify the base and exponents in the expression \$5^{-3} \cdot 5^1\( (since \)5\( can be written as \)5^1$).
3. Apply the exponent addition rule: \$5^{-3} \cdot 5^1 = 5^{-3 + 1}$.
4. Simplify the exponent by performing the addition: \(-3 + 1 = -2\), so the expression becomes \$5^{-2}$.
5. Rewrite the expression with a negative exponent as a fraction: \$5^{-2} = \frac{1}{5^2}$.

Key Concepts

Exponents and Powers

Exponents indicate how many times a base number is multiplied by itself. For example, 5^3 means 5 multiplied by itself three times (5 × 5 × 5). Understanding this helps in evaluating expressions involving powers.

Negative Exponents

A negative exponent means taking the reciprocal of the base raised to the positive exponent. For instance, 5^(-3) equals 1 divided by 5^3, or 1/(5 × 5 × 5). This concept is essential for simplifying expressions with negative powers.

Multiplication of Exponential Expressions with the Same Base

When multiplying exponential expressions with the same base, add their exponents. For example, 5^a × 5^b = 5^(a+b). This rule simplifies the evaluation of expressions like 5^(-3) × 5.