Solve frac{12^{4}*12^{7}+frac{36^{11}}{3^{11}}}{12^15/12^11+2^11*6^11}

$$\frac { 12 ^ { 4 } \cdot 12 ^ { 7 } + \frac { 36 ^ { 11 } } { 3 ^ { 11 } } } { \frac { 12 ^ { 15 } } { 12 ^ { 11 } } + 2 ^ { 11 } \cdot 6 ^ { 11 } }$$

Evaluate

$$\frac{71663616}{35831809}\approx 1.999999944$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 4 and 7 to get 11.

$$\frac{12^{11}+\frac{36^{11}}{3^{11}}}{\frac{12^{15}}{12^{11}}+2^{11}\times 6^{11}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 11 from 15 to get 4.

$$\frac{12^{11}+\frac{36^{11}}{3^{11}}}{12^{4}+2^{11}\times 6^{11}}$$

Calculate 12 to the power of 11 and get 743008370688.

$$\frac{743008370688+\frac{36^{11}}{3^{11}}}{12^{4}+2^{11}\times 6^{11}}$$

Calculate 36 to the power of 11 and get 131621703842267136.

$$\frac{743008370688+\frac{131621703842267136}{3^{11}}}{12^{4}+2^{11}\times 6^{11}}$$

Calculate 3 to the power of 11 and get 177147.

$$\frac{743008370688+\frac{131621703842267136}{177147}}{12^{4}+2^{11}\times 6^{11}}$$

Divide 131621703842267136 by 177147 to get 743008370688.

$$\frac{743008370688+743008370688}{12^{4}+2^{11}\times 6^{11}}$$

Add 743008370688 and 743008370688 to get 1486016741376.

$$\frac{1486016741376}{12^{4}+2^{11}\times 6^{11}}$$

Calculate 12 to the power of 4 and get 20736.

$$\frac{1486016741376}{20736+2^{11}\times 6^{11}}$$

Calculate 2 to the power of 11 and get 2048.

$$\frac{1486016741376}{20736+2048\times 6^{11}}$$

Calculate 6 to the power of 11 and get 362797056.

$$\frac{1486016741376}{20736+2048\times 362797056}$$

Multiply 2048 and 362797056 to get 743008370688.

$$\frac{1486016741376}{20736+743008370688}$$

Add 20736 and 743008370688 to get 743008391424.

$$\frac{1486016741376}{743008391424}$$

Reduce the fraction \frac{1486016741376}{743008391424} to lowest terms by extracting and canceling out 20736.

$$\frac{71663616}{35831809}$$

Factor

$$\frac{2 ^ {15} \cdot 3 ^ {7}}{13 \cdot 211 \cdot 13063} = 1\frac{35831807}{35831809} = 1.9999999441836722$$