Solve frac{2^{3}*4^{3}*2^-1*8}{2*8^-2*8^0*2^6}=

$$\frac { 2 ^ { 3 } \cdot 4 ^ { 3 } \cdot 2 ^ { - 1 } \cdot 8 } { 2 \cdot 8 ^ { - 2 } \cdot 8 ^ { 0 } \cdot 2 ^ { 6 } } =$$

Evaluate

$$1024$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and -1 to get 2.

$$\frac{2^{2}\times 4^{3}\times 8}{2\times 8^{-2}\times 8^{0}\times 2^{6}}$$

To multiply powers of the same base, add their exponents. Add 1 and 6 to get 7.

$$\frac{2^{2}\times 4^{3}\times 8}{2^{7}\times 8^{-2}\times 8^{0}}$$

To multiply powers of the same base, add their exponents. Add -2 and 0 to get -2.

$$\frac{2^{2}\times 4^{3}\times 8}{2^{7}\times 8^{-2}}$$

Cancel out 2^{2} in both numerator and denominator.

$$\frac{8\times 4^{3}}{2^{5}\times 8^{-2}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\frac{4^{3}\times 8^{3}}{2^{5}}$$

Calculate 4 to the power of 3 and get 64.

$$\frac{64\times 8^{3}}{2^{5}}$$

Calculate 8 to the power of 3 and get 512.

$$\frac{64\times 512}{2^{5}}$$

Multiply 64 and 512 to get 32768.

$$\frac{32768}{2^{5}}$$

Calculate 2 to the power of 5 and get 32.

$$\frac{32768}{32}$$

Divide 32768 by 32 to get 1024.

$$1024$$

Factor

$$2^{10}$$