Solve (frac{1/64*frac{sqrt{16}}{1})}{8^-2}*(16/1)^-frac{1{2}}+frac{sqrt{64}}{2^4*2^-1}

$$\frac { ( \frac { 1 } { 64 } \cdot \frac { \sqrt { 16 } } { 1 } ) } { 8 ^ { - 2 } } \cdot ( \frac { 16 } { 1 } ) ^ { - \frac { 1 } { 2 } } + \frac { \sqrt { 64 } } { 2 ^ { 4 } \cdot 2 ^ { - 1 } }$$

Evaluate

$$2$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 4 and -1 to get 3.

$$\frac{\frac{1}{64}\times \frac{\sqrt{16}}{1}}{8^{-2}}\times \left(\frac{16}{1}\right)^{-\frac{1}{2}}+\frac{\sqrt{64}}{2^{3}}$$

Calculate the square root of 16 and get 4.

$$\frac{\frac{1}{64}\times \frac{4}{1}}{8^{-2}}\times \left(\frac{16}{1}\right)^{-\frac{1}{2}}+\frac{\sqrt{64}}{2^{3}}$$

Anything divided by one gives itself.

$$\frac{\frac{1}{64}\times 4}{8^{-2}}\times \left(\frac{16}{1}\right)^{-\frac{1}{2}}+\frac{\sqrt{64}}{2^{3}}$$

Multiply \frac{1}{64} and 4 to get \frac{1}{16}.

$$\frac{\frac{1}{16}}{8^{-2}}\times \left(\frac{16}{1}\right)^{-\frac{1}{2}}+\frac{\sqrt{64}}{2^{3}}$$

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

$$\frac{\frac{1}{16}}{\frac{1}{64}}\times \left(\frac{16}{1}\right)^{-\frac{1}{2}}+\frac{\sqrt{64}}{2^{3}}$$

Divide \frac{1}{16} by \frac{1}{64} by multiplying \frac{1}{16} by the reciprocal of \frac{1}{64}.

$$\frac{1}{16}\times 64\times \left(\frac{16}{1}\right)^{-\frac{1}{2}}+\frac{\sqrt{64}}{2^{3}}$$

Multiply \frac{1}{16} and 64 to get 4.

$$4\times \left(\frac{16}{1}\right)^{-\frac{1}{2}}+\frac{\sqrt{64}}{2^{3}}$$

Anything divided by one gives itself.

$$4\times 16^{-\frac{1}{2}}+\frac{\sqrt{64}}{2^{3}}$$

Calculate 16 to the power of -\frac{1}{2} and get \frac{1}{4}.

$$4\times \frac{1}{4}+\frac{\sqrt{64}}{2^{3}}$$

Multiply 4 and \frac{1}{4} to get 1.

$$1+\frac{\sqrt{64}}{2^{3}}$$

Calculate the square root of 64 and get 8.

$$1+\frac{8}{2^{3}}$$

Calculate 2 to the power of 3 and get 8.

$$1+\frac{8}{8}$$

Divide 8 by 8 to get 1.

$$1+1$$

Add 1 and 1 to get 2.

$$2$$

Factor

$$2$$