Question

write the following expression without negative exponents and without parentheses. \\((-7x)^{-2}\\)

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 \(n\). So, we can rewrite \((-7x)^{-2}\) using this rule.
\((-7x)^{-2}=\frac{1}{(-7x)^{2}}\)

Step2: Simplify the denominator

Now, we simplify \((-7x)^{2}\). Using the power of a product rule \((ab)^{n}=a^{n}b^{n}\), where \(a = - 7\), \(b=x\) and \(n = 2\), we have \((-7x)^{2}=(-7)^{2}\times x^{2}\).
Since \((-7)^{2}=49\), then \((-7x)^{2}=49x^{2}\).
So, \(\frac{1}{(-7x)^{2}}=\frac{1}{49x^{2}}\)

Answer:

\(\frac{1}{49x^{2}}\)