Question

write the following expression without negative exponents and without parentheses. (2x)^{-1}

Explanation:

Step1: Recall the negative exponent rule

The negative exponent rule states that \(a^{-n}=\frac{1}{a^{n}}\) for any non - zero real number \(a\) and positive integer \(n\). For the expression \((2x)^{-1}\), we can apply this rule. Here, \(a = 2x\) and \(n=1\).
So, \((2x)^{-1}=\frac{1}{(2x)^{1}}\)

Step2: Simplify the expression

Since \((2x)^{1}=2x\), the expression \(\frac{1}{(2x)^{1}}\) simplifies to \(\frac{1}{2x}\)

Answer:

\(\frac{1}{2x}\)