Solve (81)*3^3-(3)^111-1(243)/(9^24)(3^3)

$$\frac { ( 81 ) \times 3 ^ { 3 } - ( 3 ) ^ { 111 - 1 } ( 243 ) } { ( 9 ^ { 24 } ) ( 3 ^ { 3 } ) }$$

Evaluate

$$-\frac{3381391913522726342930221472392241170198527451848560}{984770902183611232881}\approx -3.43368382 \cdot 10^{30}$$

Solution Steps

Calculate 3 to the power of 3 and get 27.

$$\frac{81\times 27-3^{111-1}\times 243}{9^{24}\times 3^{3}}$$

Multiply 81 and 27 to get 2187.

$$\frac{2187-3^{111-1}\times 243}{9^{24}\times 3^{3}}$$

Subtract 1 from 111 to get 110.

$$\frac{2187-3^{110}\times 243}{9^{24}\times 3^{3}}$$

Calculate 3 to the power of 110 and get 30432527221704537086371993251530170531786747066637049.

$$\frac{2187-30432527221704537086371993251530170531786747066637049\times 243}{9^{24}\times 3^{3}}$$

Multiply 30432527221704537086371993251530170531786747066637049 and 243 to get 7395104114874202511988394360121831439224179537192802907.

$$\frac{2187-7395104114874202511988394360121831439224179537192802907}{9^{24}\times 3^{3}}$$

Subtract 7395104114874202511988394360121831439224179537192802907 from 2187 to get -7395104114874202511988394360121831439224179537192800720.

$$\frac{-7395104114874202511988394360121831439224179537192800720}{9^{24}\times 3^{3}}$$

Calculate 9 to the power of 24 and get 79766443076872509863361.

$$\frac{-7395104114874202511988394360121831439224179537192800720}{79766443076872509863361\times 3^{3}}$$

Calculate 3 to the power of 3 and get 27.

$$\frac{-7395104114874202511988394360121831439224179537192800720}{79766443076872509863361\times 27}$$

Multiply 79766443076872509863361 and 27 to get 2153693963075557766310747.

$$\frac{-7395104114874202511988394360121831439224179537192800720}{2153693963075557766310747}$$

Reduce the fraction \frac{-7395104114874202511988394360121831439224179537192800720}{2153693963075557766310747} to lowest terms by extracting and canceling out 2187.

$$-\frac{3381391913522726342930221472392241170198527451848560}{984770902183611232881}$$

Factor

$$-\frac{3381391913522726342930221472392241170198527451848560}{984770902183611232881} = -3.4336838202925124 \times 10^{30}\frac{3.9279500830574694 \times 10^{20}}{9.847709021836112 \times 10^{20}} = -3.4336838202925124 \times 10^{30}$$