To find the quotient of [tex]\(\frac{7^{-1}}{7^{-2}}\)[/tex], follow these steps:
1. Understand the property of exponents: [tex]\(a^{-m} = \frac{1}{a^m}\)[/tex]. Using this property, we can rewrite the exponents:
[tex]\[
7^{-1} = \frac{1}{7^1} = \frac{1}{7}
\][/tex]
[tex]\[
7^{-2} = \frac{1}{7^2} = \frac{1}{49}
\][/tex]
2. Substitute these values back into the original expression:
[tex]\[
\frac{7^{-1}}{7^{-2}} = \frac{\frac{1}{7}}{\frac{1}{49}}
\][/tex]
3. Divide the two fractions. When you divide by a fraction, you multiply by its reciprocal:
[tex]\[
\frac{\frac{1}{7}}{\frac{1}{49}} = \frac{1}{7} \times 49 = \frac{49}{7}
\][/tex]
4. Simplify the fraction:
[tex]\[
\frac{49}{7} = 7
\][/tex]
Hence, the quotient is [tex]\(7\)[/tex]. Therefore, the answer is:
[tex]\[
\boxed{7}
\][/tex]
