Solve (20/11)^4+1/(11)^20=

$$( \frac { 20 } { 11 } ) ^ { 4 } + \frac { 1 } { ( 11 ) ^ { 20 } } =$$

Evaluate

$$\frac{7351956778171545760001}{672749994932560009201}\approx 10.928215286$$

Solution Steps

Calculate \frac{20}{11} to the power of 4 and get \frac{160000}{14641}.

$$\frac{160000}{14641}+\frac{1}{11^{20}}$$

Calculate 11 to the power of 20 and get 672749994932560009201.

$$\frac{160000}{14641}+\frac{1}{672749994932560009201}$$

Least common multiple of 14641 and 672749994932560009201 is 672749994932560009201. Convert \frac{160000}{14641} and \frac{1}{672749994932560009201} to fractions with denominator 672749994932560009201.

$$\frac{7351956778171545760000}{672749994932560009201}+\frac{1}{672749994932560009201}$$

Since \frac{7351956778171545760000}{672749994932560009201} and \frac{1}{672749994932560009201} have the same denominator, add them by adding their numerators.

$$\frac{7351956778171545760000+1}{672749994932560009201}$$

Add 7351956778171545760000 and 1 to get 7351956778171545760001.

$$\frac{7351956778171545760001}{672749994932560009201}$$

Factor

$$\frac{1097 \cdot 10529 \cdot 636515805084377}{11 ^ {20}} = 10\frac{6.24456828845945 \times 10^{20}}{6.7274999493256 \times 10^{20}} = 10.92821528584113$$