Solve 81*8/3*(3^12)^2*4^7

$$\frac { 81 \cdot 8 } { 3 \cdot ( 3 ^ { 12 } ) ^ { 2 } \cdot 4 ^ { 7 } }$$

Evaluate

$$\frac{1}{21422803359744}\approx 4.667923162 \cdot 10^{-14}$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 12 and 2 to get 24.

$$\frac{81\times 8}{3\times 3^{24}\times 4^{7}}$$

To multiply powers of the same base, add their exponents. Add 1 and 24 to get 25.

$$\frac{81\times 8}{3^{25}\times 4^{7}}$$

Multiply 81 and 8 to get 648.

$$\frac{648}{3^{25}\times 4^{7}}$$

Calculate 3 to the power of 25 and get 847288609443.

$$\frac{648}{847288609443\times 4^{7}}$$

Calculate 4 to the power of 7 and get 16384.

$$\frac{648}{847288609443\times 16384}$$

Multiply 847288609443 and 16384 to get 13881976577114112.

$$\frac{648}{13881976577114112}$$

Reduce the fraction \frac{648}{13881976577114112} to lowest terms by extracting and canceling out 648.

$$\frac{1}{21422803359744}$$

Factor

$$\frac{1}{2 ^ {11} \cdot 3 ^ {21}} = 4.667923162097073 \times 10^{-14}$$