Solve frac{3^{4}*2^{7}*8^3}{2^3+(2^3)^3}=

$$\frac { 3 ^ { 4 } \cdot 2 ^ { 7 } \cdot 8 ^ { 3 } } { 2 ^ { 3 } + ( 2 ^ { 3 } ) ^ { 3 } } =$$

Evaluate

$$\frac{663552}{65}\approx 10208.492307692$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.

$$\frac{3^{4}\times 2^{7}\times 8^{3}}{2^{3}+2^{9}}$$

Calculate 3 to the power of 4 and get 81.

$$\frac{81\times 2^{7}\times 8^{3}}{2^{3}+2^{9}}$$

Calculate 2 to the power of 7 and get 128.

$$\frac{81\times 128\times 8^{3}}{2^{3}+2^{9}}$$

Multiply 81 and 128 to get 10368.

$$\frac{10368\times 8^{3}}{2^{3}+2^{9}}$$

Calculate 8 to the power of 3 and get 512.

$$\frac{10368\times 512}{2^{3}+2^{9}}$$

Multiply 10368 and 512 to get 5308416.

$$\frac{5308416}{2^{3}+2^{9}}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{5308416}{8+2^{9}}$$

Calculate 2 to the power of 9 and get 512.

$$\frac{5308416}{8+512}$$

Add 8 and 512 to get 520.

$$\frac{5308416}{520}$$

Reduce the fraction \frac{5308416}{520} to lowest terms by extracting and canceling out 8.

$$\frac{663552}{65}$$

Factor

$$\frac{2 ^ {13} \cdot 3 ^ {4}}{5 \cdot 13} = 10208\frac{32}{65} = 10208.492307692308$$