Solve (4)^73/8+97/16+117/12

$$( 4 ) ^ { 7 } \frac { 3 } { 8 } + 9 \frac { 7 } { 16 } + 11 \frac { 7 } { 12 }$$

Evaluate

$$\frac{295921}{48}\approx 6165.020833333$$

Solution Steps

Calculate 4 to the power of 7 and get 16384.

$$16384\times \frac{3}{8}+\frac{9\times 16+7}{16}+\frac{11\times 12+7}{12}$$

Express 16384\times \frac{3}{8} as a single fraction.

$$\frac{16384\times 3}{8}+\frac{9\times 16+7}{16}+\frac{11\times 12+7}{12}$$

Multiply 16384 and 3 to get 49152.

$$\frac{49152}{8}+\frac{9\times 16+7}{16}+\frac{11\times 12+7}{12}$$

Divide 49152 by 8 to get 6144.

$$6144+\frac{9\times 16+7}{16}+\frac{11\times 12+7}{12}$$

Multiply 9 and 16 to get 144.

$$6144+\frac{144+7}{16}+\frac{11\times 12+7}{12}$$

Add 144 and 7 to get 151.

$$6144+\frac{151}{16}+\frac{11\times 12+7}{12}$$

Convert 6144 to fraction \frac{98304}{16}.

$$\frac{98304}{16}+\frac{151}{16}+\frac{11\times 12+7}{12}$$

Since \frac{98304}{16} and \frac{151}{16} have the same denominator, add them by adding their numerators.

$$\frac{98304+151}{16}+\frac{11\times 12+7}{12}$$

Add 98304 and 151 to get 98455.

$$\frac{98455}{16}+\frac{11\times 12+7}{12}$$

Multiply 11 and 12 to get 132.

$$\frac{98455}{16}+\frac{132+7}{12}$$

Add 132 and 7 to get 139.

$$\frac{98455}{16}+\frac{139}{12}$$

Least common multiple of 16 and 12 is 48. Convert \frac{98455}{16} and \frac{139}{12} to fractions with denominator 48.

$$\frac{295365}{48}+\frac{556}{48}$$

Since \frac{295365}{48} and \frac{556}{48} have the same denominator, add them by adding their numerators.

$$\frac{295365+556}{48}$$

Add 295365 and 556 to get 295921.

$$\frac{295921}{48}$$

Factor

$$\frac{223 \cdot 1327}{2 ^ {4} \cdot 3} = 6165\frac{1}{48} = 6165.020833333333$$