Question

write the expression with only positive exponents and evaluate if possible. assume all variables represent nonzero numbers.
6x⁻²
6x⁻² = \square (type exponential notation with positive exponents )

Explanation:

Step1: Recall the negative exponent rule

The negative exponent rule states that \(a^{-n}=\frac{1}{a^{n}}\) for any non - zero number \(a\) and positive integer \(n\). In the expression \(6x^{-2}\), we only apply the negative exponent rule to the term with the negative exponent, which is \(x^{-2}\). The coefficient \(6\) remains as it is.

Step2: Apply the negative exponent rule

Using the rule \(a^{-n}=\frac{1}{a^{n}}\) with \(a = x\) and \(n=2\), we can rewrite \(x^{-2}\) as \(\frac{1}{x^{2}}\). So, \(6x^{-2}=6\times\frac{1}{x^{2}}\)

Step3: Simplify the expression

\(6\times\frac{1}{x^{2}}=\frac{6}{x^{2}}\)

Answer:

\(\frac{6}{x^{2}}\)