Solve 1/4+left(1+left(4left(1+3^-1right)^-1right)^-1right)^-1

$$\frac{ 1 }{ 4 } + { \left(1+ { \left(4 { \left(1+ { 3 }^{ -1 } \right) }^{ -1 } \right) }^{ -1 } \right) }^{ -1 }$$

Evaluate

$$1$$

Solution Steps

Calculate 3 to the power of -1 and get \frac{1}{3}.

$$\frac{1}{4}+\left(1+\left(4\left(1+\frac{1}{3}\right)^{-1}\right)^{-1}\right)^{-1}$$

Add 1 and \frac{1}{3} to get \frac{4}{3}.

$$\frac{1}{4}+\left(1+\left(4\times \left(\frac{4}{3}\right)^{-1}\right)^{-1}\right)^{-1}$$

Calculate \frac{4}{3} to the power of -1 and get \frac{3}{4}.

$$\frac{1}{4}+\left(1+\left(4\times \frac{3}{4}\right)^{-1}\right)^{-1}$$

Multiply 4 and \frac{3}{4} to get 3.

$$\frac{1}{4}+\left(1+3^{-1}\right)^{-1}$$

Calculate 3 to the power of -1 and get \frac{1}{3}.

$$\frac{1}{4}+\left(1+\frac{1}{3}\right)^{-1}$$

Add 1 and \frac{1}{3} to get \frac{4}{3}.

$$\frac{1}{4}+\left(\frac{4}{3}\right)^{-1}$$

Calculate \frac{4}{3} to the power of -1 and get \frac{3}{4}.

$$\frac{1}{4}+\frac{3}{4}$$

Add \frac{1}{4} and \frac{3}{4} to get 1.

$$1$$

Factor

$$1$$