Solve -1^5/5--1^4/4-8^-1/3+6

$$\frac{ - { 1 }^{ 5 } }{ 5 } - \frac{ - { 1 }^{ 4 } }{ 4 } - \frac{ { 8 }^{ -1 } }{ 3 } +6$$

Evaluate

$$\frac{721}{120}\approx 6.008333333$$

Solution Steps

Calculate 1 to the power of 5 and get 1.

$$\frac{-1}{5}-\frac{-1^{4}}{4}-\frac{8^{-1}}{3}+6$$

Fraction \frac{-1}{5} can be rewritten as -\frac{1}{5} by extracting the negative sign.

$$-\frac{1}{5}-\frac{-1^{4}}{4}-\frac{8^{-1}}{3}+6$$

Calculate 1 to the power of 4 and get 1.

$$-\frac{1}{5}-\frac{-1}{4}-\frac{8^{-1}}{3}+6$$

Fraction \frac{-1}{4} can be rewritten as -\frac{1}{4} by extracting the negative sign.

$$-\frac{1}{5}-\left(-\frac{1}{4}\right)-\frac{8^{-1}}{3}+6$$

The opposite of -\frac{1}{4} is \frac{1}{4}.

$$-\frac{1}{5}+\frac{1}{4}-\frac{8^{-1}}{3}+6$$

Add -\frac{1}{5} and \frac{1}{4} to get \frac{1}{20}.

$$\frac{1}{20}-\frac{8^{-1}}{3}+6$$

Calculate 8 to the power of -1 and get \frac{1}{8}.

$$\frac{1}{20}-\frac{\frac{1}{8}}{3}+6$$

Express \frac{\frac{1}{8}}{3} as a single fraction.

$$\frac{1}{20}-\frac{1}{8\times 3}+6$$

Multiply 8 and 3 to get 24.

$$\frac{1}{20}-\frac{1}{24}+6$$

Subtract \frac{1}{24} from \frac{1}{20} to get \frac{1}{120}.

$$\frac{1}{120}+6$$

Add \frac{1}{120} and 6 to get \frac{721}{120}.

$$\frac{721}{120}$$

Factor

$$\frac{7 \cdot 103}{2 ^ {3} \cdot 3 \cdot 5} = 6\frac{1}{120} = 6.008333333333334$$