Solve 1-{1-[1/6-31/5*(-1/4)^2]*30}div(-1)^2005

$$1 - \{ 1 - [ \frac { 1 } { 6 } - 3 \frac { 1 } { 5 } \times ( - \frac { 1 } { 4 } ) ^ { 2 } ] \times 30 \} \div ( - 1 ) ^ { 2005 }$$

Evaluate

$$3$$

Solution Steps

Multiply 3 and 5 to get 15.

$$1-\frac{1-\left(\frac{1}{6}-\frac{15+1}{5}\left(-\frac{1}{4}\right)^{2}\right)\times 30}{\left(-1\right)^{2005}}$$

Add 15 and 1 to get 16.

$$1-\frac{1-\left(\frac{1}{6}-\frac{16}{5}\left(-\frac{1}{4}\right)^{2}\right)\times 30}{\left(-1\right)^{2005}}$$

Calculate -\frac{1}{4} to the power of 2 and get \frac{1}{16}.

$$1-\frac{1-\left(\frac{1}{6}-\frac{16}{5}\times \frac{1}{16}\right)\times 30}{\left(-1\right)^{2005}}$$

Multiply \frac{16}{5} times \frac{1}{16} by multiplying numerator times numerator and denominator times denominator.

$$1-\frac{1-\left(\frac{1}{6}-\frac{16\times 1}{5\times 16}\right)\times 30}{\left(-1\right)^{2005}}$$

Cancel out 16 in both numerator and denominator.

$$1-\frac{1-\left(\frac{1}{6}-\frac{1}{5}\right)\times 30}{\left(-1\right)^{2005}}$$

Least common multiple of 6 and 5 is 30. Convert \frac{1}{6} and \frac{1}{5} to fractions with denominator 30.

$$1-\frac{1-\left(\frac{5}{30}-\frac{6}{30}\right)\times 30}{\left(-1\right)^{2005}}$$

Since \frac{5}{30} and \frac{6}{30} have the same denominator, subtract them by subtracting their numerators.

$$1-\frac{1-\frac{5-6}{30}\times 30}{\left(-1\right)^{2005}}$$

Subtract 6 from 5 to get -1.

$$1-\frac{1-\left(-\frac{1}{30}\times 30\right)}{\left(-1\right)^{2005}}$$

Cancel out 30 and 30.

$$1-\frac{1-\left(-1\right)}{\left(-1\right)^{2005}}$$

The opposite of -1 is 1.

$$1-\frac{1+1}{\left(-1\right)^{2005}}$$

Add 1 and 1 to get 2.

$$1-\frac{2}{\left(-1\right)^{2005}}$$

Calculate -1 to the power of 2005 and get -1.

$$1-\frac{2}{-1}$$

Fraction \frac{2}{-1} can be rewritten as -2 by extracting the negative sign.

$$1-\left(-2\right)$$

The opposite of -2 is 2.

$$1+2$$

Add 1 and 2 to get 3.

$$3$$

Factor

$$3$$