To simplify the expression [tex]\(8^2 \times 3^{-6} \times\left(2^{-3}\right)^2\)[/tex], we will break it down and simplify each part step by step.
1. Simplify [tex]\(8^2\)[/tex]:
[tex]\[
8^2 = 64
\][/tex]
2. Simplify [tex]\(3^{-6}\)[/tex]:
- A negative exponent indicates that we take the reciprocal of the base raised to the positive exponent.
[tex]\[
3^{-6} = \frac{1}{3^6} \approx 0.0013717421124828531
\][/tex]
3. Simplify [tex]\(\left(2^{-3}\right)^2\)[/tex]:
- First, simplify inside the parentheses: [tex]\(2^{-3}\)[/tex].
[tex]\[
2^{-3} = \frac{1}{2^3} = \frac{1}{8}
\][/tex]
- Then, raise [tex]\(\frac{1}{8}\)[/tex] to the power of 2.
[tex]\[
\left(\frac{1}{8}\right)^2 = \frac{1}{8^2} = \frac{1}{64} \approx 0.015625
\][/tex]
4. Multiply all the simplified terms:
[tex]\[
64 \times 0.0013717421124828531 \times 0.015625 \approx 0.0013717421124828531
\][/tex]
Thus, the simplified form of the expression [tex]\(8^2 \times 3^{-6} \times\left(2^{-3}\right)^2\)[/tex] is approximately [tex]\(0.0013717421124828531\)[/tex].
