Solve frac{4^{-7}*16*32^3}{2^6*8^3*64^-2}

$$\frac { 4 ^ { - 7 } \cdot 16 \cdot 32 ^ { 3 } } { 2 ^ { 6 } \cdot 8 ^ { 3 } \cdot 64 ^ { - 2 } }$$

Evaluate

$$4$$

Solution Steps

Calculate 4 to the power of -7 and get \frac{1}{16384}.

$$\frac{\frac{1}{16384}\times 16\times 32^{3}}{2^{6}\times 8^{3}\times 64^{-2}}$$

Multiply \frac{1}{16384} and 16 to get \frac{1}{1024}.

$$\frac{\frac{1}{1024}\times 32^{3}}{2^{6}\times 8^{3}\times 64^{-2}}$$

Calculate 32 to the power of 3 and get 32768.

$$\frac{\frac{1}{1024}\times 32768}{2^{6}\times 8^{3}\times 64^{-2}}$$

Multiply \frac{1}{1024} and 32768 to get 32.

$$\frac{32}{2^{6}\times 8^{3}\times 64^{-2}}$$

Calculate 2 to the power of 6 and get 64.

$$\frac{32}{64\times 8^{3}\times 64^{-2}}$$

Calculate 8 to the power of 3 and get 512.

$$\frac{32}{64\times 512\times 64^{-2}}$$

Multiply 64 and 512 to get 32768.

$$\frac{32}{32768\times 64^{-2}}$$

Calculate 64 to the power of -2 and get \frac{1}{4096}.

$$\frac{32}{32768\times \frac{1}{4096}}$$

Multiply 32768 and \frac{1}{4096} to get 8.

$$\frac{32}{8}$$

Divide 32 by 8 to get 4.

$$4$$

Factor

$$2^{2}$$