To solve the problem of representing [tex]\(\frac{1}{16} \times \frac{1}{8}\)[/tex] using exponential notation, let's break it down step-by-step.
First, let's express each fraction in terms of powers of 2:
1. [tex]\(\frac{1}{16}\)[/tex]:
[tex]\[ \frac{1}{16} = \frac{1}{2^4} = 2^{-4} \][/tex]
2. [tex]\(\frac{1}{8}\)[/tex]:
[tex]\[ \frac{1}{8} = \frac{1}{2^3} = 2^{-3} \][/tex]
Now, we'll multiply the two fractions:
[tex]\[ \frac{1}{16} \times \frac{1}{8} = 2^{-4} \times 2^{-3} \][/tex]
When multiplying expressions with the same base, we add the exponents:
[tex]\[ 2^{-4} \times 2^{-3} = 2^{(-4) + (-3)} = 2^{-7} \][/tex]
Hence, the correct exponential notation for [tex]\(\frac{1}{16} \times \frac{1}{8}\)[/tex] is [tex]\(\left(2^{-4}\right)\left(2^{-3}\right)\)[/tex].
So, the correct answer is:
[tex]\(\left(2^{-4}\right)\left(2^{-3}\right)\)[/tex]
