Question

Use the Negative Exponent Rule to generate an equivalent expression to 3−12
. Write your answer in radical form.(1 point)
3−12 =

Answer 1

To apply the Negative Exponent Rule, we know that \( a^{-n} = \frac{1}{a^n} \).

For the expression \( 3^{-12} \):

\[
3^{-12} = \frac{1}{3^{12}}
\]

Now, to express \( 3^{12} \) in radical form, we note that \( 3^{12} \) can be written as \( (3^6)^2 \). Therefore, we can rewrite it using radicals:

\[
3^{12} = (3^6)^2
\]

Thus, the radical form of \( 3^{-12} \) becomes:

\[
3^{-12} = \frac{1}{3^{12}} = \frac{1}{(3^6)^2} = \frac{1}{\sqrt{3^{12}}} = \frac{1}{\sqrt{(3^6)^2}}
\]

However, to keep it simple and concise, we can just express it as:

\[
3^{-12} = \frac{1}{3^{12}} = \frac{1}{3^{12}} = \frac{1}{\sqrt{3^{24}}}
\]

So, the final answer in radical form is:

\[
3^{-12} = \frac{1}{3^{12}} \text{ or } \sqrt{3^{24}}
\]

Thus, the equivalent expression for \( 3^{-12} \) in radical form is:

\[
\frac{1}{3^{12}}
\]

Or expressed as a square root:

\[
\frac{1}{\sqrt{3^{24}}}
\]

Final answer in standard form:

\[
3^{-12} = \frac{1}{3^{12}}
\]