Write each expression without negative exponents, and evaluate if possible. Assume all variables represent nonzero real numbers. See Example 4. (1/3)^-2

Key Concepts

Negative Exponents

Negative exponents indicate the reciprocal of the base raised to the absolute value of the exponent. For example, a^-n = 1/a^n. This concept is crucial for rewriting expressions without negative exponents, as it allows us to transform them into a more standard form that is easier to evaluate.

Reciprocal

The reciprocal of a number is defined as 1 divided by that number. In the context of exponents, when dealing with negative exponents, we take the reciprocal of the base raised to the positive exponent. For instance, (1/3)^-2 becomes 3^2, which simplifies the expression for evaluation.

Evaluating Expressions

Evaluating an expression involves calculating its value based on the given numbers and operations. In this case, after rewriting the expression without negative exponents, we can substitute the values and perform the necessary arithmetic operations to find the final result, ensuring clarity and accuracy in the solution.