Solve (2/11)^10*2/11+(55/10)^1+0

$$( \frac { 2 } { 11 } ) ^ { 10 } \times \frac { 2 } { 11 } + ( \frac { 55 } { 10 } ) ^ { 1 + 0 }$$

Evaluate

$$\frac{3138428380817}{570623341222}\approx 5.500000007$$

Solution Steps

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

$$\left(\frac{2}{11}\right)^{11}+\left(\frac{55}{10}\right)^{1+0}$$

Calculate \frac{2}{11} to the power of 11 and get \frac{2048}{285311670611}.

$$\frac{2048}{285311670611}+\left(\frac{55}{10}\right)^{1+0}$$

Reduce the fraction \frac{55}{10} to lowest terms by extracting and canceling out 5.

$$\frac{2048}{285311670611}+\left(\frac{11}{2}\right)^{1+0}$$

Add 1 and 0 to get 1.

$$\frac{2048}{285311670611}+\left(\frac{11}{2}\right)^{1}$$

Calculate \frac{11}{2} to the power of 1 and get \frac{11}{2}.

$$\frac{2048}{285311670611}+\frac{11}{2}$$

Add \frac{2048}{285311670611} and \frac{11}{2} to get \frac{3138428380817}{570623341222}.

$$\frac{3138428380817}{570623341222}$$

Factor

$$\frac{97 \cdot 601 \cdot 3673 \cdot 14657}{2 \cdot 11 ^ {11}} = 5\frac{285311674707}{570623341222} = 5.500000007178115$$