Solve frac{3^{45}+1}{(3^{30}-3^15+1)*(3^10-3^5+1)^-1}

$$\frac { 3 ^ { 45 } + 1 } { ( 3 ^ { 30 } - 3 ^ { 15 } + 1 ) \cdot ( 3 ^ { 10 } - 3 ^ { 5 } + 1 ) ^ { - 1 } }$$

Evaluate

$$843816232756$$

Solution Steps

Calculate 3 to the power of 45 and get 2954312706550833698643.

$$\frac{2954312706550833698643+1}{\left(3^{30}-3^{15}+1\right)\left(3^{10}-3^{5}+1\right)^{-1}}$$

Add 2954312706550833698643 and 1 to get 2954312706550833698644.

$$\frac{2954312706550833698644}{\left(3^{30}-3^{15}+1\right)\left(3^{10}-3^{5}+1\right)^{-1}}$$

Calculate 3 to the power of 30 and get 205891132094649.

$$\frac{2954312706550833698644}{\left(205891132094649-3^{15}+1\right)\left(3^{10}-3^{5}+1\right)^{-1}}$$

Calculate 3 to the power of 15 and get 14348907.

$$\frac{2954312706550833698644}{\left(205891132094649-14348907+1\right)\left(3^{10}-3^{5}+1\right)^{-1}}$$

Subtract 14348907 from 205891132094649 to get 205891117745742.

$$\frac{2954312706550833698644}{\left(205891117745742+1\right)\left(3^{10}-3^{5}+1\right)^{-1}}$$

Add 205891117745742 and 1 to get 205891117745743.

$$\frac{2954312706550833698644}{205891117745743\left(3^{10}-3^{5}+1\right)^{-1}}$$

Calculate 3 to the power of 10 and get 59049.

$$\frac{2954312706550833698644}{205891117745743\left(59049-3^{5}+1\right)^{-1}}$$

Calculate 3 to the power of 5 and get 243.

$$\frac{2954312706550833698644}{205891117745743\left(59049-243+1\right)^{-1}}$$

Subtract 243 from 59049 to get 58806.

$$\frac{2954312706550833698644}{205891117745743\left(58806+1\right)^{-1}}$$

Add 58806 and 1 to get 58807.

$$\frac{2954312706550833698644}{205891117745743\times 58807^{-1}}$$

Calculate 58807 to the power of -1 and get \frac{1}{58807}.

$$\frac{2954312706550833698644}{205891117745743\times \frac{1}{58807}}$$

Multiply 205891117745743 and \frac{1}{58807} to get \frac{205891117745743}{58807}.

$$\frac{2954312706550833698644}{\frac{205891117745743}{58807}}$$

Divide 2954312706550833698644 by \frac{205891117745743}{58807} by multiplying 2954312706550833698644 by the reciprocal of \frac{205891117745743}{58807}.

$$2954312706550833698644\times \frac{58807}{205891117745743}$$

Multiply 2954312706550833698644 and \frac{58807}{205891117745743} to get 843816232756.

$$843816232756$$

Factor

$$2^{2}\times 7^{2}\times 31^{2}\times 61\times 271^{2}$$