Write each expression without negative exponents, and evaluate if possible. Assume all variables represent nonzero real numbers. 4x^-2

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Identify the expression given: \(4x^{-2}\). The negative exponent indicates the reciprocal of the base raised to the positive exponent.

Rewrite the expression by applying the rule \(a^{-n} = \frac{1}{a^n}\), so \(x^{-2}\) becomes \(\frac{1}{x^2}\).

Substitute this back into the expression to get \(4 \times \frac{1}{x^2}\).

Simplify the expression by writing it as a single fraction: \(\frac{4}{x^2}\).

Since the problem states to evaluate if possible and variables represent nonzero real numbers, this is the simplified form without negative exponents.

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주요 개념

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Negative Exponents

A negative exponent indicates the reciprocal of the base raised to the corresponding positive exponent. For example, x⁻² equals 1/x². Understanding this allows rewriting expressions without negative exponents by moving factors between numerator and denominator.

Simplifying Algebraic Expressions

Simplifying involves rewriting expressions in a more straightforward form by applying exponent rules and combining like terms. This process helps in expressing terms without negative exponents and prepares the expression for evaluation.

Evaluating Expressions with Variables

Evaluating an expression means substituting given values for variables and calculating the result. Since variables are nonzero, division by zero is avoided, ensuring the expression with negative exponents rewritten as fractions can be safely evaluated.

Write each expression without negative exponents, and evaluate if possible. Assume all variables represent nonzero real numbers. 4x-2