To determine the reciprocal of the product of the fractions [tex]\(\frac{-3}{8} \times \frac{-7}{13}\)[/tex], let's break it down into a detailed solution:
1. Compute the product of the fractions:
The multiplication of two fractions is done by multiplying their numerators together and their denominators together:
[tex]\[
\frac{-3}{8} \times \frac{-7}{13} = \frac{(-3) \times (-7)}{8 \times 13}
\][/tex]
2. Simplify the product:
Simplifying the above expression:
[tex]\[
\frac{-3 \times -7}{8 \times 13} = \frac{21}{104}
\][/tex]
3. Find the reciprocal of the product:
The reciprocal of a fraction [tex]\(\frac{a}{b}\)[/tex] is found by flipping the numerator and the denominator, giving [tex]\(\frac{b}{a}\)[/tex]. Therefore, the reciprocal of [tex]\(\frac{21}{104}\)[/tex] is:
[tex]\[
\frac{104}{21}
\][/tex]
4. Verify which option matches the reciprocal:
We are given the options to select from:
[tex]\[
\text{a) } \frac{104}{21} \quad \text{b) } \frac{-104}{21} \quad \text{c) } \frac{21}{104} \quad \text{d) } \frac{-21}{104}
\][/tex]
From our calculations, the correct reciprocal of the product [tex]\(\frac{21}{104}\)[/tex] is [tex]\(\frac{104}{21}\)[/tex], which matches option (a).
Therefore, the correct answer is (a) [tex]\(\frac{104}{21}\)[/tex].
