Sure, let's rewrite the given expression [tex]\(5^{-9}\)[/tex] with a positive exponent.
1. Identify the given expression:
[tex]\[
5^{-9}
\][/tex]
2. Recall the property of negative exponents:
When you have a negative exponent, [tex]\(a^{-b}\)[/tex], it can be rewritten as:
[tex]\[
a^{-b} = \frac{1}{a^b}
\][/tex]
3. Apply this property to the given expression:
Replace [tex]\(5^{-9}\)[/tex] with [tex]\(\frac{1}{5^9}\)[/tex]:
[tex]\[
5^{-9} = \frac{1}{5^9}
\][/tex]
4. Simplify the expression inside the denominator if needed:
Although it's not always necessary to compute the value of [tex]\(5^9\)[/tex] exactly for rewriting purposes, the rewritten form in fraction is:
[tex]\[
\frac{1}{5^9}
\][/tex]
Thus, the expression [tex]\(5^{-9}\)[/tex] when rewritten with a positive exponent becomes:
[tex]\[
5^{-9} = \frac{1}{5^9}
\][/tex]
The calculated numerical value of this expression is approximately [tex]\(5.12 \times 10^{-7}\)[/tex] or [tex]\(5.12e-07\)[/tex], but for the purpose of rewriting with a positive exponent alone, the boxed answer is:
[tex]\[
\boxed{\frac{1}{5^9}}
\][/tex]
