Question

rewrite the expression without using a negative exponent.
-6n^{-2}
simplify your answer as much as possible.

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). In the expression \( -6n^{-2} \), we apply this rule to the term with the negative exponent, which is \( n^{-2} \).

Step2: Apply the negative exponent rule to \( n^{-2} \)

Using the rule \( a^{-n}=\frac{1}{a^{n}} \), for \( a = n \) and \( n=2 \), we have \( n^{-2}=\frac{1}{n^{2}} \). Now substitute this back into the original expression \( -6n^{-2} \).

So, \( -6n^{-2}=-6\times\frac{1}{n^{2}} \)

Step3: Simplify the expression

Multiplying -6 and \( \frac{1}{n^{2}} \), we get \( \frac{-6}{n^{2}} \) or \( -\frac{6}{n^{2}} \)

Answer:

\( -\dfrac{6}{n^{2}} \)