Question

write the following expression without negative exponents and without parentheses. (-6x)^{-2}

Explanation:

Step1: Recall the negative exponent rule

The rule for negative exponents is \(a^{-n}=\frac{1}{a^{n}}\) (where \(a
eq0\) and \(n\) is a positive integer). So we can rewrite \((-6x)^{-2}\) using this rule.
\((-6x)^{-2}=\frac{1}{(-6x)^{2}}\)

Step2: Simplify the denominator

Now we simplify \((-6x)^{2}\). Using the power of a product rule \((ab)^{n}=a^{n}b^{n}\), we have \((-6x)^{2}=(-6)^{2}x^{2}\).
Calculating \((-6)^{2}\), we get \((-6)\times(-6) = 36\). So \((-6)^{2}x^{2}=36x^{2}\).
Putting it back into the fraction, we have \(\frac{1}{36x^{2}}\).

Answer:

\(\frac{1}{36x^{2}}\)