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 definition of negative exponents: for any nonzero number \(a\) and positive integer \(n\), \(a^{-n} = \frac{1}{a^n}\).
2. Apply this definition to the expression \$5^{-2}\(. According to the rule, \)5^{-2} = \frac{1}{5^2}$.
3. Examine the given equation: \$5^{-2} = \frac{1}{5^2}$. Both sides match the definition of negative exponents.
4. Since the equation correctly applies the negative exponent rule, the statement is true.
5. No correction is needed because the equation is already correct.

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 means 5^-2 equals 1 divided by 5 squared.

Order of Operations and Exponentiation

Exponentiation is performed before division or multiplication. When interpreting expressions like 1/5^2, the exponent applies only to the base 5, not the entire denominator unless parentheses indicate otherwise.

Evaluating and Comparing Expressions

To determine if an equation is true, evaluate both sides separately. For 5^-2 and 1/5^2, calculate each value to verify equality. This process helps identify if the statement is true or requires correction.