Solve 5(-1/5)^4-34(-1/5)^3-2(-5/5)^2+6(1/5)+2

$$5 ( - \frac { 1 } { 5 } ) ^ { 4 } - 34 ( - \frac { 1 } { 5 } ) ^ { 3 } - 2 ( - \frac { 5 } { 5 } ) ^ { 2 } + 6 ( \frac { 1 } { 5 } ) + 2$$

Evaluate

$$\frac{37}{25}=1.48$$

Solution Steps

Divide 5 by 5 to get 1.

$$5\left(-\frac{1}{5}\right)^{4}-34\left(-\frac{1}{5}\right)^{3}-2\left(-1\right)^{2}+6\times \frac{1}{5}+2$$

Calculate -\frac{1}{5} to the power of 4 and get \frac{1}{625}.

$$5\times \frac{1}{625}-34\left(-\frac{1}{5}\right)^{3}-2\left(-1\right)^{2}+6\times \frac{1}{5}+2$$

Multiply 5 and \frac{1}{625} to get \frac{1}{125}.

$$\frac{1}{125}-34\left(-\frac{1}{5}\right)^{3}-2\left(-1\right)^{2}+6\times \frac{1}{5}+2$$

Calculate -\frac{1}{5} to the power of 3 and get -\frac{1}{125}.

$$\frac{1}{125}-34\left(-\frac{1}{125}\right)-2\left(-1\right)^{2}+6\times \frac{1}{5}+2$$

Multiply 34 and -\frac{1}{125} to get -\frac{34}{125}.

$$\frac{1}{125}-\left(-\frac{34}{125}\right)-2\left(-1\right)^{2}+6\times \frac{1}{5}+2$$

The opposite of -\frac{34}{125} is \frac{34}{125}.

$$\frac{1}{125}+\frac{34}{125}-2\left(-1\right)^{2}+6\times \frac{1}{5}+2$$

Add \frac{1}{125} and \frac{34}{125} to get \frac{7}{25}.

$$\frac{7}{25}-2\left(-1\right)^{2}+6\times \frac{1}{5}+2$$

Calculate -1 to the power of 2 and get 1.

$$\frac{7}{25}-2\times 1+6\times \frac{1}{5}+2$$

Multiply 2 and 1 to get 2.

$$\frac{7}{25}-2+6\times \frac{1}{5}+2$$

Subtract 2 from \frac{7}{25} to get -\frac{43}{25}.

$$-\frac{43}{25}+6\times \frac{1}{5}+2$$

Multiply 6 and \frac{1}{5} to get \frac{6}{5}.

$$-\frac{43}{25}+\frac{6}{5}+2$$

Add -\frac{43}{25} and \frac{6}{5} to get -\frac{13}{25}.

$$-\frac{13}{25}+2$$

Add -\frac{13}{25} and 2 to get \frac{37}{25}.

$$\frac{37}{25}$$

Factor

$$\frac{37}{5 ^ {2}} = 1\frac{12}{25} = 1.48$$