Solve (3+1/2)(3^2+1/7)(3^4+1/2)(3^8+1/8)=

$$( 3 + \frac { 1 } { 2 } ) ( 3 ^ { 2 } + \frac { 1 } { 7 } ) ( 3 ^ { 4 } + \frac { 1 } { 2 } ) ( 3 ^ { 8 } + \frac { 1 } { 8 } ) =$$

Evaluate

$$17111414$$

Solution Steps

Convert 3 to fraction \frac{6}{2}.

$$\left(\frac{6}{2}+\frac{1}{2}\right)\left(3^{2}+\frac{1}{7}\right)\left(3^{4}+\frac{1}{2}\right)\left(3^{8}+\frac{1}{8}\right)$$

Since \frac{6}{2} and \frac{1}{2} have the same denominator, add them by adding their numerators.

$$\frac{6+1}{2}\left(3^{2}+\frac{1}{7}\right)\left(3^{4}+\frac{1}{2}\right)\left(3^{8}+\frac{1}{8}\right)$$

Add 6 and 1 to get 7.

$$\frac{7}{2}\left(3^{2}+\frac{1}{7}\right)\left(3^{4}+\frac{1}{2}\right)\left(3^{8}+\frac{1}{8}\right)$$

Calculate 3 to the power of 2 and get 9.

$$\frac{7}{2}\left(9+\frac{1}{7}\right)\left(3^{4}+\frac{1}{2}\right)\left(3^{8}+\frac{1}{8}\right)$$

Convert 9 to fraction \frac{63}{7}.

$$\frac{7}{2}\left(\frac{63}{7}+\frac{1}{7}\right)\left(3^{4}+\frac{1}{2}\right)\left(3^{8}+\frac{1}{8}\right)$$

Since \frac{63}{7} and \frac{1}{7} have the same denominator, add them by adding their numerators.

$$\frac{7}{2}\times \frac{63+1}{7}\left(3^{4}+\frac{1}{2}\right)\left(3^{8}+\frac{1}{8}\right)$$

Add 63 and 1 to get 64.

$$\frac{7}{2}\times \frac{64}{7}\left(3^{4}+\frac{1}{2}\right)\left(3^{8}+\frac{1}{8}\right)$$

Multiply \frac{7}{2} times \frac{64}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7\times 64}{2\times 7}\left(3^{4}+\frac{1}{2}\right)\left(3^{8}+\frac{1}{8}\right)$$

Cancel out 7 in both numerator and denominator.

$$\frac{64}{2}\left(3^{4}+\frac{1}{2}\right)\left(3^{8}+\frac{1}{8}\right)$$

Divide 64 by 2 to get 32.

$$32\left(3^{4}+\frac{1}{2}\right)\left(3^{8}+\frac{1}{8}\right)$$

Calculate 3 to the power of 4 and get 81.

$$32\left(81+\frac{1}{2}\right)\left(3^{8}+\frac{1}{8}\right)$$

Convert 81 to fraction \frac{162}{2}.

$$32\left(\frac{162}{2}+\frac{1}{2}\right)\left(3^{8}+\frac{1}{8}\right)$$

Since \frac{162}{2} and \frac{1}{2} have the same denominator, add them by adding their numerators.

$$32\times \frac{162+1}{2}\left(3^{8}+\frac{1}{8}\right)$$

Add 162 and 1 to get 163.

$$32\times \frac{163}{2}\left(3^{8}+\frac{1}{8}\right)$$

Express 32\times \frac{163}{2} as a single fraction.

$$\frac{32\times 163}{2}\left(3^{8}+\frac{1}{8}\right)$$

Multiply 32 and 163 to get 5216.

$$\frac{5216}{2}\left(3^{8}+\frac{1}{8}\right)$$

Divide 5216 by 2 to get 2608.

$$2608\left(3^{8}+\frac{1}{8}\right)$$

Calculate 3 to the power of 8 and get 6561.

$$2608\left(6561+\frac{1}{8}\right)$$

Convert 6561 to fraction \frac{52488}{8}.

$$2608\left(\frac{52488}{8}+\frac{1}{8}\right)$$

Since \frac{52488}{8} and \frac{1}{8} have the same denominator, add them by adding their numerators.

$$2608\times \frac{52488+1}{8}$$

Add 52488 and 1 to get 52489.

$$2608\times \frac{52489}{8}$$

Express 2608\times \frac{52489}{8} as a single fraction.

$$\frac{2608\times 52489}{8}$$

Multiply 2608 and 52489 to get 136891312.

$$\frac{136891312}{8}$$

Divide 136891312 by 8 to get 17111414.

$$17111414$$

Factor

$$2\times 163\times 52489$$