Solve frac{(3^{15}+3^13)*2^9}{(3^14+3^12)*1024}

$$\frac { ( 3 ^ { 15 } + 3 ^ { 13 } ) \cdot 2 ^ { 9 } } { ( 3 ^ { 14 } + 3 ^ { 12 } ) \cdot 1024 }$$

Evaluate

$$\frac{3}{2}=1.5$$

Solution Steps

Calculate 3 to the power of 15 and get 14348907.

$$\frac{\left(14348907+3^{13}\right)\times 2^{9}}{\left(3^{14}+3^{12}\right)\times 1024}$$

Calculate 3 to the power of 13 and get 1594323.

$$\frac{\left(14348907+1594323\right)\times 2^{9}}{\left(3^{14}+3^{12}\right)\times 1024}$$

Add 14348907 and 1594323 to get 15943230.

$$\frac{15943230\times 2^{9}}{\left(3^{14}+3^{12}\right)\times 1024}$$

Calculate 2 to the power of 9 and get 512.

$$\frac{15943230\times 512}{\left(3^{14}+3^{12}\right)\times 1024}$$

Multiply 15943230 and 512 to get 8162933760.

$$\frac{8162933760}{\left(3^{14}+3^{12}\right)\times 1024}$$

Calculate 3 to the power of 14 and get 4782969.

$$\frac{8162933760}{\left(4782969+3^{12}\right)\times 1024}$$

Calculate 3 to the power of 12 and get 531441.

$$\frac{8162933760}{\left(4782969+531441\right)\times 1024}$$

Add 4782969 and 531441 to get 5314410.

$$\frac{8162933760}{5314410\times 1024}$$

Multiply 5314410 and 1024 to get 5441955840.

$$\frac{8162933760}{5441955840}$$

Reduce the fraction \frac{8162933760}{5441955840} to lowest terms by extracting and canceling out 2720977920.

$$\frac{3}{2}$$

Factor

$$\frac{3}{2} = 1\frac{1}{2} = 1.5$$