Simplify \(\sqrt{\frac{1}{64}}\) to \(\frac{\sqrt{1}}{\sqrt{64}}\).
\[\frac{{2}^{-3}}{\frac{\sqrt{1}}{\sqrt{64}}}\sin{45}\]
Simplify \(\sqrt{1}\) to \(1\).
\[\frac{{2}^{-3}}{\frac{1}{\sqrt{64}}}\sin{45}\]
Since \(8\times 8=64\), the square root of \(64\) is \(8\).
\[\frac{{2}^{-3}}{\frac{1}{8}}\sin{45}\]
Use Negative Power Rule: \({x}^{-a}=\frac{1}{{x}^{a}}\).
\[\frac{\frac{1}{{2}^{3}}}{\frac{1}{8}}\sin{45}\]
Simplify \({2}^{3}\) to \(8\).
\[\frac{\frac{1}{8}}{\frac{1}{8}}\sin{45}\]
Cancel denominators.
\[1\times \sin{45}\]
Simplify.
\[\sin{45}\]
Decimal Form: 0.850904
sin(45)
