Solve -3^101*(1/3)^100*(-1)^201-1/3

$$- 3 ^ { 101 } \times ( \frac { 1 } { 3 } ) ^ { 100 } \times ( - 1 ) ^ { 201 } - \frac { 1 } { 3 }$$

Evaluate

$$\frac{8}{3}\approx 2.666666667$$

Solution Steps

Calculate 3 to the power of 101 and get 1546132562196033993109383389296863818106322566003.

$$-1546132562196033993109383389296863818106322566003\times \left(\frac{1}{3}\right)^{100}\left(-1\right)^{201}-\frac{1}{3}$$

Calculate \frac{1}{3} to the power of 100 and get \frac{1}{515377520732011331036461129765621272702107522001}.

$$-1546132562196033993109383389296863818106322566003\times \frac{1}{515377520732011331036461129765621272702107522001}\left(-1\right)^{201}-\frac{1}{3}$$

Multiply -1546132562196033993109383389296863818106322566003 and \frac{1}{515377520732011331036461129765621272702107522001} to get \frac{-1546132562196033993109383389296863818106322566003}{515377520732011331036461129765621272702107522001}.

$$\frac{-1546132562196033993109383389296863818106322566003}{515377520732011331036461129765621272702107522001}\left(-1\right)^{201}-\frac{1}{3}$$

Divide -1546132562196033993109383389296863818106322566003 by 515377520732011331036461129765621272702107522001 to get -3.

$$-3\left(-1\right)^{201}-\frac{1}{3}$$

Calculate -1 to the power of 201 and get -1.

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

Multiply -3 and -1 to get 3.

$$3-\frac{1}{3}$$

Convert 3 to fraction \frac{9}{3}.

$$\frac{9}{3}-\frac{1}{3}$$

Since \frac{9}{3} and \frac{1}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{9-1}{3}$$

Subtract 1 from 9 to get 8.

$$\frac{8}{3}$$

Factor

$$\frac{2 ^ {3}}{3} = 2\frac{2}{3} = 2.6666666666666665$$