Solve frac{3*2^{6}*2^{4}*3^{6}*3^{8}*2}{3^{3}*2^{5}*2^7*3^2*2^2*3^3}=

$$\frac { 3 \cdot 2 ^ { 6 } \cdot 2 ^ { 4 } \cdot 3 ^ { 6 } \cdot 3 ^ { 8 } \cdot 2 } { 3 ^ { 3 } \cdot 2 ^ { 5 } \cdot 2 ^ { 7 } \cdot 3 ^ { 2 } \cdot 2 ^ { 2 } \cdot 3 ^ { 3 } } =$$

Evaluate

$$\frac{2187}{8}=273.375$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 6 to get 7.

$$\frac{3^{7}\times 2^{6}\times 2^{4}\times 3^{8}\times 2}{3^{3}\times 2^{5}\times 2^{7}\times 3^{2}\times 2^{2}\times 3^{3}}$$

To multiply powers of the same base, add their exponents. Add 7 and 8 to get 15.

$$\frac{3^{15}\times 2^{6}\times 2^{4}\times 2}{3^{3}\times 2^{5}\times 2^{7}\times 3^{2}\times 2^{2}\times 3^{3}}$$

To multiply powers of the same base, add their exponents. Add 6 and 4 to get 10.

$$\frac{3^{15}\times 2^{10}\times 2}{3^{3}\times 2^{5}\times 2^{7}\times 3^{2}\times 2^{2}\times 3^{3}}$$

To multiply powers of the same base, add their exponents. Add 10 and 1 to get 11.

$$\frac{3^{15}\times 2^{11}}{3^{3}\times 2^{5}\times 2^{7}\times 3^{2}\times 2^{2}\times 3^{3}}$$

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

$$\frac{3^{15}\times 2^{11}}{3^{5}\times 2^{5}\times 2^{7}\times 2^{2}\times 3^{3}}$$

To multiply powers of the same base, add their exponents. Add 5 and 3 to get 8.

$$\frac{3^{15}\times 2^{11}}{3^{8}\times 2^{5}\times 2^{7}\times 2^{2}}$$

To multiply powers of the same base, add their exponents. Add 5 and 7 to get 12.

$$\frac{3^{15}\times 2^{11}}{3^{8}\times 2^{12}\times 2^{2}}$$

To multiply powers of the same base, add their exponents. Add 12 and 2 to get 14.

$$\frac{3^{15}\times 2^{11}}{3^{8}\times 2^{14}}$$

Cancel out 2^{11}\times 3^{8} in both numerator and denominator.

$$\frac{3^{7}}{2^{3}}$$

Calculate 3 to the power of 7 and get 2187.

$$\frac{2187}{2^{3}}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{2187}{8}$$

Factor

$$\frac{3 ^ {7}}{2 ^ {3}} = 273\frac{3}{8} = 273.375$$