Solve (3/4)^10*(11/3)^11

$$( \frac { 3 } { 4 } ) ^ { 10 } \cdot ( 1 \frac { 1 } { 3 } ) ^ { 11 }$$

Evaluate

$$\frac{4}{3}\approx 1.333333333$$

Solution Steps

Calculate \frac{3}{4} to the power of 10 and get \frac{59049}{1048576}.

$$\frac{59049}{1048576}\times \left(\frac{1\times 3+1}{3}\right)^{11}$$

Multiply 1 and 3 to get 3.

$$\frac{59049}{1048576}\times \left(\frac{3+1}{3}\right)^{11}$$

Add 3 and 1 to get 4.

$$\frac{59049}{1048576}\times \left(\frac{4}{3}\right)^{11}$$

Calculate \frac{4}{3} to the power of 11 and get \frac{4194304}{177147}.

$$\frac{59049}{1048576}\times \frac{4194304}{177147}$$

Multiply \frac{59049}{1048576} and \frac{4194304}{177147} to get \frac{4}{3}.

$$\frac{4}{3}$$

Factor

$$\frac{2 ^ {2}}{3} = 1\frac{1}{3} = 1.3333333333333333$$