Solve 9^24+1/3^16-3^8+1-1-9*9^3

$$\frac { 9 ^ { 24 } + 1 } { 3 ^ { 16 } - 3 ^ { 8 } + 1 } - 1 - 9 \cdot 9 ^ { 3 }$$

Evaluate

$$\frac{79766443076590080326880}{43040161}\approx 1.853302618 \cdot 10^{15}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 3 to get 4.

$$\frac{9^{24}+1}{3^{16}-3^{8}+1}-1-9^{4}$$

Calculate 9 to the power of 24 and get 79766443076872509863361.

$$\frac{79766443076872509863361+1}{3^{16}-3^{8}+1}-1-9^{4}$$

Add 79766443076872509863361 and 1 to get 79766443076872509863362.

$$\frac{79766443076872509863362}{3^{16}-3^{8}+1}-1-9^{4}$$

Calculate 3 to the power of 16 and get 43046721.

$$\frac{79766443076872509863362}{43046721-3^{8}+1}-1-9^{4}$$

Calculate 3 to the power of 8 and get 6561.

$$\frac{79766443076872509863362}{43046721-6561+1}-1-9^{4}$$

Subtract 6561 from 43046721 to get 43040160.

$$\frac{79766443076872509863362}{43040160+1}-1-9^{4}$$

Add 43040160 and 1 to get 43040161.

$$\frac{79766443076872509863362}{43040161}-1-9^{4}$$

Convert 1 to fraction \frac{43040161}{43040161}.

$$\frac{79766443076872509863362}{43040161}-\frac{43040161}{43040161}-9^{4}$$

Since \frac{79766443076872509863362}{43040161} and \frac{43040161}{43040161} have the same denominator, subtract them by subtracting their numerators.

$$\frac{79766443076872509863362-43040161}{43040161}-9^{4}$$

Subtract 43040161 from 79766443076872509863362 to get 79766443076872466823201.

$$\frac{79766443076872466823201}{43040161}-9^{4}$$

Calculate 9 to the power of 4 and get 6561.

$$\frac{79766443076872466823201}{43040161}-6561$$

Convert 6561 to fraction \frac{282386496321}{43040161}.

$$\frac{79766443076872466823201}{43040161}-\frac{282386496321}{43040161}$$

Since \frac{79766443076872466823201}{43040161} and \frac{282386496321}{43040161} have the same denominator, subtract them by subtracting their numerators.

$$\frac{79766443076872466823201-282386496321}{43040161}$$

Subtract 282386496321 from 79766443076872466823201 to get 79766443076590080326880.

$$\frac{79766443076590080326880}{43040161}$$

Factor

$$\frac{2 ^ {5} \cdot 3 ^ {24} \cdot 5 \cdot 7 \cdot 13 \cdot 41 \cdot 73 \cdot 6481}{97 \cdot 577 \cdot 769} = 1853302618375198\frac{6325026}{43040161} = 1853302618375198.2$$