Determine whether each statement is true or false. If false, correct the right side of the equation. 5^-2 = 1/5²

Verified step by step guidance

1. Recall the rule for negative exponents: for any nonzero number \(a\) and integer \(n\), \(a^{-n} = \frac{1}{a^n}\).
2. Apply this rule to the expression \$5^{-2}$, which means \(5^{-2} = \frac{1}{5^2}\).
3. Compare the given equation \(5^{-2} = \frac{1}{5^2}\) with the rule and see if they match.
4. Since the right side of the equation is \(\frac{1}{5^2}\), which matches the rule, the statement is true.
5. Therefore, no correction is needed because the equation correctly represents the negative exponent.

Key Concepts

Negative Exponents

A negative exponent indicates the reciprocal of the base raised to the corresponding positive exponent. For example, a^{-n} = 1/a^n, where a ≠ 0. This rule helps rewrite expressions with negative powers into fractions.

Exponentiation Rules

Exponentiation rules govern how to manipulate powers, including product, quotient, and power of a power rules. Understanding these rules ensures correct simplification and transformation of expressions involving exponents.

Evaluating and Comparing Expressions

Evaluating expressions means calculating their numerical value or rewriting them in equivalent forms. Comparing expressions involves checking if two expressions represent the same value, which is essential for determining the truth of equations.