Solve (9-1/3*4/3^2)+(4-1/3*4/4^2)+(frac{5-1}{3}*frac{4}{5^3})+(frac{6*1}{3}*frac{4}{6^2})+(frac{2*1}{3}*frac{4}{22})

$$( \frac { 9 - 1 } { 3 } \cdot \frac { 4 } { 3 ^ { 2 } } ) + ( \frac { 4 - 1 } { 3 } \cdot \frac { 4 } { 4 ^ { 2 } } ) + ( \frac { 5 - 1 } { 3 } \cdot \frac { 4 } { 5 ^ { 3 } } ) + ( \frac { 6 \cdot 1 } { 3 } \cdot \frac { 4 } { 6 ^ { 2 } } ) + ( \frac { 2 \cdot 1 } { 3 } \cdot \frac { 4 } { 22 } )$$

Evaluate

$$\frac{270461}{148500}\approx 1.821286195$$

Solution Steps

Rewrite 4^{2} as 4\times 4. Cancel out 4 in both numerator and denominator.

$$\frac{9-1}{3}\times \frac{4}{3^{2}}+\frac{4-1}{3}\times \frac{1}{4}+\frac{5-1}{3}\times \frac{4}{5^{3}}+\frac{6\times 1}{3}\times \frac{4}{6^{2}}+\frac{2\times 1}{3}\times \frac{4}{22}$$

Subtract 1 from 9 to get 8.

$$\frac{8}{3}\times \frac{4}{3^{2}}+\frac{4-1}{3}\times \frac{1}{4}+\frac{5-1}{3}\times \frac{4}{5^{3}}+\frac{6\times 1}{3}\times \frac{4}{6^{2}}+\frac{2\times 1}{3}\times \frac{4}{22}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{8}{3}\times \frac{4}{9}+\frac{4-1}{3}\times \frac{1}{4}+\frac{5-1}{3}\times \frac{4}{5^{3}}+\frac{6\times 1}{3}\times \frac{4}{6^{2}}+\frac{2\times 1}{3}\times \frac{4}{22}$$

Multiply \frac{8}{3} times \frac{4}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{8\times 4}{3\times 9}+\frac{4-1}{3}\times \frac{1}{4}+\frac{5-1}{3}\times \frac{4}{5^{3}}+\frac{6\times 1}{3}\times \frac{4}{6^{2}}+\frac{2\times 1}{3}\times \frac{4}{22}$$

Do the multiplications in the fraction \frac{8\times 4}{3\times 9}.

$$\frac{32}{27}+\frac{4-1}{3}\times \frac{1}{4}+\frac{5-1}{3}\times \frac{4}{5^{3}}+\frac{6\times 1}{3}\times \frac{4}{6^{2}}+\frac{2\times 1}{3}\times \frac{4}{22}$$

Subtract 1 from 4 to get 3.

$$\frac{32}{27}+\frac{3}{3}\times \frac{1}{4}+\frac{5-1}{3}\times \frac{4}{5^{3}}+\frac{6\times 1}{3}\times \frac{4}{6^{2}}+\frac{2\times 1}{3}\times \frac{4}{22}$$

Divide 3 by 3 to get 1.

$$\frac{32}{27}+1\times \frac{1}{4}+\frac{5-1}{3}\times \frac{4}{5^{3}}+\frac{6\times 1}{3}\times \frac{4}{6^{2}}+\frac{2\times 1}{3}\times \frac{4}{22}$$

Multiply 1 and \frac{1}{4} to get \frac{1}{4}.

$$\frac{32}{27}+\frac{1}{4}+\frac{5-1}{3}\times \frac{4}{5^{3}}+\frac{6\times 1}{3}\times \frac{4}{6^{2}}+\frac{2\times 1}{3}\times \frac{4}{22}$$

Least common multiple of 27 and 4 is 108. Convert \frac{32}{27} and \frac{1}{4} to fractions with denominator 108.

$$\frac{128}{108}+\frac{27}{108}+\frac{5-1}{3}\times \frac{4}{5^{3}}+\frac{6\times 1}{3}\times \frac{4}{6^{2}}+\frac{2\times 1}{3}\times \frac{4}{22}$$

Since \frac{128}{108} and \frac{27}{108} have the same denominator, add them by adding their numerators.

$$\frac{128+27}{108}+\frac{5-1}{3}\times \frac{4}{5^{3}}+\frac{6\times 1}{3}\times \frac{4}{6^{2}}+\frac{2\times 1}{3}\times \frac{4}{22}$$

Add 128 and 27 to get 155.

$$\frac{155}{108}+\frac{5-1}{3}\times \frac{4}{5^{3}}+\frac{6\times 1}{3}\times \frac{4}{6^{2}}+\frac{2\times 1}{3}\times \frac{4}{22}$$

Subtract 1 from 5 to get 4.

$$\frac{155}{108}+\frac{4}{3}\times \frac{4}{5^{3}}+\frac{6\times 1}{3}\times \frac{4}{6^{2}}+\frac{2\times 1}{3}\times \frac{4}{22}$$

Calculate 5 to the power of 3 and get 125.

$$\frac{155}{108}+\frac{4}{3}\times \frac{4}{125}+\frac{6\times 1}{3}\times \frac{4}{6^{2}}+\frac{2\times 1}{3}\times \frac{4}{22}$$

Multiply \frac{4}{3} times \frac{4}{125} by multiplying numerator times numerator and denominator times denominator.

$$\frac{155}{108}+\frac{4\times 4}{3\times 125}+\frac{6\times 1}{3}\times \frac{4}{6^{2}}+\frac{2\times 1}{3}\times \frac{4}{22}$$

Do the multiplications in the fraction \frac{4\times 4}{3\times 125}.

$$\frac{155}{108}+\frac{16}{375}+\frac{6\times 1}{3}\times \frac{4}{6^{2}}+\frac{2\times 1}{3}\times \frac{4}{22}$$

Least common multiple of 108 and 375 is 13500. Convert \frac{155}{108} and \frac{16}{375} to fractions with denominator 13500.

$$\frac{19375}{13500}+\frac{576}{13500}+\frac{6\times 1}{3}\times \frac{4}{6^{2}}+\frac{2\times 1}{3}\times \frac{4}{22}$$

Since \frac{19375}{13500} and \frac{576}{13500} have the same denominator, add them by adding their numerators.

$$\frac{19375+576}{13500}+\frac{6\times 1}{3}\times \frac{4}{6^{2}}+\frac{2\times 1}{3}\times \frac{4}{22}$$

Add 19375 and 576 to get 19951.

$$\frac{19951}{13500}+\frac{6\times 1}{3}\times \frac{4}{6^{2}}+\frac{2\times 1}{3}\times \frac{4}{22}$$

Multiply 6 and 1 to get 6.

$$\frac{19951}{13500}+\frac{6}{3}\times \frac{4}{6^{2}}+\frac{2\times 1}{3}\times \frac{4}{22}$$

Divide 6 by 3 to get 2.

$$\frac{19951}{13500}+2\times \frac{4}{6^{2}}+\frac{2\times 1}{3}\times \frac{4}{22}$$

Calculate 6 to the power of 2 and get 36.

$$\frac{19951}{13500}+2\times \frac{4}{36}+\frac{2\times 1}{3}\times \frac{4}{22}$$

Reduce the fraction \frac{4}{36} to lowest terms by extracting and canceling out 4.

$$\frac{19951}{13500}+2\times \frac{1}{9}+\frac{2\times 1}{3}\times \frac{4}{22}$$

Multiply 2 and \frac{1}{9} to get \frac{2}{9}.

$$\frac{19951}{13500}+\frac{2}{9}+\frac{2\times 1}{3}\times \frac{4}{22}$$

Least common multiple of 13500 and 9 is 13500. Convert \frac{19951}{13500} and \frac{2}{9} to fractions with denominator 13500.

$$\frac{19951}{13500}+\frac{3000}{13500}+\frac{2\times 1}{3}\times \frac{4}{22}$$

Since \frac{19951}{13500} and \frac{3000}{13500} have the same denominator, add them by adding their numerators.

$$\frac{19951+3000}{13500}+\frac{2\times 1}{3}\times \frac{4}{22}$$

Add 19951 and 3000 to get 22951.

$$\frac{22951}{13500}+\frac{2\times 1}{3}\times \frac{4}{22}$$

Multiply 2 and 1 to get 2.

$$\frac{22951}{13500}+\frac{2}{3}\times \frac{4}{22}$$

Reduce the fraction \frac{4}{22} to lowest terms by extracting and canceling out 2.

$$\frac{22951}{13500}+\frac{2}{3}\times \frac{2}{11}$$

Multiply \frac{2}{3} times \frac{2}{11} by multiplying numerator times numerator and denominator times denominator.

$$\frac{22951}{13500}+\frac{2\times 2}{3\times 11}$$

Do the multiplications in the fraction \frac{2\times 2}{3\times 11}.

$$\frac{22951}{13500}+\frac{4}{33}$$

Least common multiple of 13500 and 33 is 148500. Convert \frac{22951}{13500} and \frac{4}{33} to fractions with denominator 148500.

$$\frac{252461}{148500}+\frac{18000}{148500}$$

Since \frac{252461}{148500} and \frac{18000}{148500} have the same denominator, add them by adding their numerators.

$$\frac{252461+18000}{148500}$$

Add 252461 and 18000 to get 270461.

$$\frac{270461}{148500}$$

Factor

$$\frac{270461}{2 ^ {2} \cdot 3 ^ {3} \cdot 5 ^ {3} \cdot 11} = 1\frac{121961}{148500} = 1.8212861952861952$$