Solve frac{frac{frac{frac{frac{frac{frac{frac{frac{frac{frac{frac{2/2^2/left(2^2right)^2//}{}}{}}{}}{}}{}}{}}{}}{}}{}}{}}{}}{}

$$\frac{ \frac{ \frac{ \frac{ \frac{ \frac{ \frac{ \frac{ \frac{ \frac{ \frac{ \frac{ \frac{ \frac{ \frac{ \frac{ 2 }{ { 2 }^{ 2 } } }{ { \left( { 2 }^{ 2 } \right) }^{ 2 } } }{ } }{ } }{ } }{ } }{ } }{ } }{ } }{ } }{ } }{ } }{ } }{ } }{ } }{ }$$

Evaluate

$$\frac{1}{32}=0.03125$$

Solution Steps

Rewrite 2^{2} as 2\times 2. Cancel out 2 in both numerator and denominator.

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

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{1}{2}}{2^{4}}}{1}}{1}}{1}}{1}}{1}}{1}}{1}}{1}}{1}}{1}}{1}}{1}}{1}}{1}$$

Calculate 2 to the power of 4 and get 16.

$$\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{1}{2}}{16}}{1}}{1}}{1}}{1}}{1}}{1}}{1}}{1}}{1}}{1}}{1}}{1}}{1}}{1}$$

Express \frac{\frac{1}{2}}{16} as a single fraction.

$$\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{1}{2\times 16}}{1}}{1}}{1}}{1}}{1}}{1}}{1}}{1}}{1}}{1}}{1}}{1}}{1}}{1}$$

Multiply 2 and 16 to get 32.

$$\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{1}{32}}{1}}{1}}{1}}{1}}{1}}{1}}{1}}{1}}{1}}{1}}{1}}{1}}{1}}{1}$$

Anything divided by one gives itself.

$$\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{1}{32}}{1}}{1}}{1}}{1}}{1}}{1}}{1}}{1}}{1}}{1}}{1}}{1}}{1}$$

Anything divided by one gives itself.

$$\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{1}{32}}{1}}{1}}{1}}{1}}{1}}{1}}{1}}{1}}{1}}{1}}{1}}{1}$$

Anything divided by one gives itself.

$$\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{1}{32}}{1}}{1}}{1}}{1}}{1}}{1}}{1}}{1}}{1}}{1}}{1}$$

Anything divided by one gives itself.

$$\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{1}{32}}{1}}{1}}{1}}{1}}{1}}{1}}{1}}{1}}{1}}{1}$$

Anything divided by one gives itself.

$$\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{1}{32}}{1}}{1}}{1}}{1}}{1}}{1}}{1}}{1}}{1}$$

Anything divided by one gives itself.

$$\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{1}{32}}{1}}{1}}{1}}{1}}{1}}{1}}{1}}{1}$$

Anything divided by one gives itself.

$$\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{1}{32}}{1}}{1}}{1}}{1}}{1}}{1}}{1}$$

Anything divided by one gives itself.

$$\frac{\frac{\frac{\frac{\frac{\frac{\frac{1}{32}}{1}}{1}}{1}}{1}}{1}}{1}$$

Anything divided by one gives itself.

$$\frac{\frac{\frac{\frac{\frac{\frac{1}{32}}{1}}{1}}{1}}{1}}{1}$$

Anything divided by one gives itself.

$$\frac{\frac{\frac{\frac{\frac{1}{32}}{1}}{1}}{1}}{1}$$

Anything divided by one gives itself.

$$\frac{\frac{\frac{\frac{1}{32}}{1}}{1}}{1}$$

Anything divided by one gives itself.

$$\frac{\frac{\frac{1}{32}}{1}}{1}$$

Anything divided by one gives itself.

$$\frac{\frac{1}{32}}{1}$$

Anything divided by one gives itself.

$$\frac{1}{32}$$

Factor

$$\frac{1}{2 ^ {5}} = 0.03125$$