Solve frac{(4)^{6}-(4^3)^4}{9^2*4^7}

$$\frac { ( 4 ) ^ { 6 } - ( 4 ^ { 3 } ) ^ { 4 } } { 9 ^ { 2 } \times 4 ^ { 7 } }$$

Evaluate

$$-\frac{455}{36}\approx -12.638888889$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 3 and 4 to get 12.

$$\frac{4^{6}-4^{12}}{9^{2}\times 4^{7}}$$

Calculate 4 to the power of 6 and get 4096.

$$\frac{4096-4^{12}}{9^{2}\times 4^{7}}$$

Calculate 4 to the power of 12 and get 16777216.

$$\frac{4096-16777216}{9^{2}\times 4^{7}}$$

Subtract 16777216 from 4096 to get -16773120.

$$\frac{-16773120}{9^{2}\times 4^{7}}$$

Calculate 9 to the power of 2 and get 81.

$$\frac{-16773120}{81\times 4^{7}}$$

Calculate 4 to the power of 7 and get 16384.

$$\frac{-16773120}{81\times 16384}$$

Multiply 81 and 16384 to get 1327104.

$$\frac{-16773120}{1327104}$$

Reduce the fraction \frac{-16773120}{1327104} to lowest terms by extracting and canceling out 36864.

$$-\frac{455}{36}$$

Factor

$$-\frac{455}{36} = -12\frac{23}{36} = -12.63888888888889$$