Sure, let's simplify the expression [tex]\(\frac{3}{a^{-2}}\)[/tex] step by step.
1. Understand the given expression:
[tex]\(\frac{3}{a^{-2}}\)[/tex]
2. Recall the property of exponents:
The negative exponent rule states that [tex]\(a^{-n} = \frac{1}{a^n}\)[/tex]. Hence, [tex]\(a^{-2} = \frac{1}{a^2}\)[/tex].
3. Substitute the expression [tex]\(a^{-2}\)[/tex] with [tex]\(\frac{1}{a^2}\)[/tex]:
[tex]\[
\frac{3}{a^{-2}} = \frac{3}{\frac{1}{a^2}}
\][/tex]
4. Simplify the fraction:
Dividing by a fraction is equivalent to multiplying by its reciprocal. So, we have:
[tex]\[
\frac{3}{\frac{1}{a^2}} = 3 \times a^2
\][/tex]
5. Result:
[tex]\[
3 \times a^2 = 3a^2
\][/tex]
Thus, the simplified form of [tex]\(\frac{3}{a^{-2}}\)[/tex] is [tex]\(3a^2\)[/tex].
