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

Verified step by step guidance

1. Start with the expression $(4x{)}^{-2}$.
2. Recall the rule for negative exponents: $a^{-n}=\frac{1}{a^n}$.
3. Apply the rule to the expression: $(4x{)}^{-2}=\frac{1}{(4x{)}^2}$.
4. Expand $(4x{)}^2$ as $(4x)\times (4x)$.
5. Simplify the expression to $\frac{1}{16x^2}$.

Key Concepts

Negative Exponents

Negative exponents indicate the reciprocal of the base raised to the absolute value of the exponent. For example, a term like a^-n can be rewritten as 1/(a^n). This concept is essential for simplifying expressions that contain negative exponents, allowing for easier evaluation and manipulation of algebraic expressions.

Exponent Rules

Exponent rules, such as the product of powers, power of a power, and power of a product, govern how to simplify expressions involving exponents. For instance, (ab)^n = a^n * b^n and (a^m)^n = a^(m*n). Understanding these rules is crucial for correctly rewriting expressions and performing calculations involving exponents.

Evaluating Expressions

Evaluating expressions involves substituting values for variables and performing arithmetic operations to find a numerical result. In the context of the given expression, after rewriting it without negative exponents, one can substitute specific values for x to compute the final result. This process is fundamental in algebra for solving equations and understanding function behavior.