Solve frac{2^8/sqrt{16}8^-2}{frac{{left(32^2right)}^frac{1{5}}}{4}}

$$\frac{ \frac{ { 2 }^{ 8 } }{ \sqrt{ 16 } } { 8 }^{ -2 } }{ \frac{ { \left( { 32 }^{ 2 } \right) }^{ \frac{ 1 }{ 5 } } }{ 4 } }$$

Evaluate

$$1$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 2 and \frac{1}{5} to get \frac{2}{5}.

$$\frac{\frac{2^{8}}{\sqrt{16}}\times 8^{-2}}{\frac{32^{\frac{2}{5}}}{4}}$$

Calculate 2 to the power of 8 and get 256.

$$\frac{\frac{256}{\sqrt{16}}\times 8^{-2}}{\frac{32^{\frac{2}{5}}}{4}}$$

Calculate the square root of 16 and get 4.

$$\frac{\frac{256}{4}\times 8^{-2}}{\frac{32^{\frac{2}{5}}}{4}}$$

Divide 256 by 4 to get 64.

$$\frac{64\times 8^{-2}}{\frac{32^{\frac{2}{5}}}{4}}$$

Calculate 8 to the power of -2 and get \frac{1}{64}.

$$\frac{64\times \frac{1}{64}}{\frac{32^{\frac{2}{5}}}{4}}$$

Multiply 64 and \frac{1}{64} to get 1.

$$\frac{1}{\frac{32^{\frac{2}{5}}}{4}}$$

Calculate 32 to the power of \frac{2}{5} and get 4.

$$\frac{1}{\frac{4}{4}}$$

Divide 4 by 4 to get 1.

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

Anything divided by one gives itself.

$$1$$

Factor

$$1$$