Answer:
[tex](\frac{4}{64^{\frac{5}{6}}})^{\frac{1}{2}}=\frac{\sqrt{2}}{4}[/tex]
Step-by-step explanation:
Exponents property : [tex](x^a)^b=x^{ab};\frac{x^c}{x^a}=x^{c-d}=\frac{1}{x^{d-c}}[/tex]
[tex](\frac{4}{64^{\frac{5}{6}}})^{\frac{1}{2}}\\4=2\times 2=2^2\\64=2\times 2\times 2\times 2\times 2\times 2=2^6\\\\64^{\frac{5}{6}}=(26)^{\frac{5}{6}}=2^{6\times \frac{5}{6}}=2^5\\\\(\frac{4}{64^{\frac{5}{6}}})^{\frac{1}{2}}=(\frac{2^2}{2^5})^{\frac{1}{2}}=(\frac{1}{2^{5-2}})^{\frac{1}{2}}=(\frac{1}{2^3})^{\frac{1}{2}}\\\\=\frac{1}{2^{\frac{3}{2}}}=\frac{1}{2\sqrt{2} }[/tex]
Multiply numerator and denominator by [tex]\sqrt{2}[/tex]
[tex](\frac{4}{64^{\frac{5}{6}}})^{\frac{1}{2}}=\frac{1}{2\sqrt{2}}\times \frac{\sqrt{2}}{\sqrt{2}}=\frac{\sqrt{2}}{4}[/tex]
