Evaluate each exponential expression: 5^(-3) • 5

Verified step by step guidance

1. Identify the base and the exponents in the expression: The base is 5, and the exponents are -3 and 1 (since 5 is the same as 5^1).
2. Apply the property of exponents that states when multiplying like bases, you add the exponents: $5^{-3}\cdot 5^1=5^{-3+1}$.
3. Simplify the exponent: $-3+1=-2$, so the expression becomes $5^{-2}$.
4. Recall the rule for negative exponents: $a^{-n}=\frac{1}{a^n}$.
5. Apply the rule for negative exponents to rewrite $5^{-2}$ as $\frac{1}{5^2}$.

Key Concepts

Exponential Notation

Exponential notation is a mathematical shorthand used to represent repeated multiplication of a number by itself. In the expression a^n, 'a' is the base and 'n' is the exponent, indicating how many times 'a' is multiplied. For example, 5^3 means 5 multiplied by itself three times, resulting in 125.

Negative Exponents

Negative exponents indicate the reciprocal of the base raised to the absolute value of the exponent. For instance, 5^(-3) is equivalent to 1/(5^3), which simplifies to 1/125. This concept is crucial for simplifying expressions involving negative exponents and understanding their impact on calculations.

Product of Powers Property

The Product of Powers Property states that when multiplying two expressions with the same base, you can add their exponents. For example, a^m • a^n = a^(m+n). In the given expression, 5^(-3) • 5 can be rewritten as 5^(-3) • 5^1, allowing us to combine the exponents to simplify the expression to 5^(-2).