To find the value of the expression [tex]\( 4^5 \times 2^3 \times 2^{-6} \)[/tex], let’s break it down into intermediate steps.
1. Evaluate [tex]\( 4^5 \)[/tex]:
[tex]\[
4^5 = 1024
\][/tex]
2. Evaluate [tex]\( 2^3 \)[/tex]:
[tex]\[
2^3 = 8
\][/tex]
3. Evaluate [tex]\( 2^{-6} \)[/tex]:
[tex]\[
2^{-6} = \frac{1}{2^6} = \frac{1}{64} = 0.015625
\][/tex]
Next, we multiply the results obtained from each step:
[tex]\[
1024 \times 8 \times 0.015625
\][/tex]
First, multiply [tex]\( 1024 \)[/tex] and [tex]\( 8 \)[/tex]:
[tex]\[
1024 \times 8 = 8192
\][/tex]
Now, multiply the result by [tex]\( 0.015625 \)[/tex]:
[tex]\[
8192 \times 0.015625 = 128.0
\][/tex]
Thus, the value of [tex]\( 4^5 \times 2^3 \times 2^{-6} \)[/tex] is:
[tex]\[
128.0
\][/tex]
