In Exercises 35–52, write each expression with positive exponents only. Then simplify, if possible.(-5)⁻²

Verified step by step guidance

1. Identify the expression with a negative exponent: \((-5)^{-2}\).
2. Recall the rule for negative exponents: \(a^{-n} = \frac{1}{a^n}\).
3. Apply the rule to the expression: \((-5)^{-2} = \frac{1}{(-5)^2}\).
4. Calculate the positive exponent: \((-5)^2 = (-5) \times (-5)\).
5. Simplify the expression: \(\frac{1}{(-5) \times (-5)}\).

Key Concepts

Negative Exponents

A negative exponent indicates that the base should be taken as the reciprocal raised to the absolute value of the exponent. For example, a⁻n = 1/aⁿ. This concept is crucial for rewriting expressions with negative exponents into forms that use only positive exponents.

Reciprocal

The reciprocal of a number is 1 divided by that number. In the context of exponents, when converting a negative exponent, the base is flipped to its reciprocal. For instance, (-5)⁻² becomes 1/(-5)², which is essential for simplifying expressions correctly.

Simplification of Exponents

Simplification involves reducing an expression to its simplest form. When dealing with exponents, this may include calculating powers and combining like terms. For example, after converting (-5)⁻² to its positive exponent form, further simplification leads to evaluating (-5)² = 25, which is a key step in the problem.