Solve {left({left(frac{1/6right)}^{5}right)}^2}{{left({left(1/2right)}^3{left(1/3right)}^3right)}^2}

$$\frac{ { \left( { \left( \frac{ 1 }{ 6 } \right) }^{ 5 } \right) }^{ 2 } }{ { \left( { \left( \frac{ 1 }{ 2 } \right) }^{ 3 } { \left( \frac{ 1 }{ 3 } \right) }^{ 3 } \right) }^{ 2 } }$$

Evaluate

$$\frac{1}{1296}\approx 0.000771605$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 5 and 2 to get 10.

$$\frac{\left(\frac{1}{6}\right)^{10}}{\left(\left(\frac{1}{2}\right)^{3}\times \left(\frac{1}{3}\right)^{3}\right)^{2}}$$

Calculate \frac{1}{6} to the power of 10 and get \frac{1}{60466176}.

$$\frac{\frac{1}{60466176}}{\left(\left(\frac{1}{2}\right)^{3}\times \left(\frac{1}{3}\right)^{3}\right)^{2}}$$

Calculate \frac{1}{2} to the power of 3 and get \frac{1}{8}.

$$\frac{\frac{1}{60466176}}{\left(\frac{1}{8}\times \left(\frac{1}{3}\right)^{3}\right)^{2}}$$

Calculate \frac{1}{3} to the power of 3 and get \frac{1}{27}.

$$\frac{\frac{1}{60466176}}{\left(\frac{1}{8}\times \frac{1}{27}\right)^{2}}$$

Multiply \frac{1}{8} and \frac{1}{27} to get \frac{1}{216}.

$$\frac{\frac{1}{60466176}}{\left(\frac{1}{216}\right)^{2}}$$

Calculate \frac{1}{216} to the power of 2 and get \frac{1}{46656}.

$$\frac{\frac{1}{60466176}}{\frac{1}{46656}}$$

Divide \frac{1}{60466176} by \frac{1}{46656} by multiplying \frac{1}{60466176} by the reciprocal of \frac{1}{46656}.

$$\frac{1}{60466176}\times 46656$$

Multiply \frac{1}{60466176} and 46656 to get \frac{1}{1296}.

$$\frac{1}{1296}$$

Factor

$$\frac{1}{2 ^ {4} \cdot 3 ^ {4}} = 0.0007716049382716049$$