Solve |-8.25-13/4|-[(-6)^3*(-1/6)^2-(-6^2)]

$$| - 8.25 - 1 \frac { 3 } { 4 } | - [ ( - 6 ) ^ { 3 } \times ( - \frac { 1 } { 6 } ) ^ { 2 } - ( - 6 ^ { 2 } ) ]$$

Evaluate

$$-20$$

Solution Steps

Multiply 1 and 4 to get 4.

$$|-8.25-\frac{4+3}{4}|-\left(\left(-6\right)^{3}\left(-\frac{1}{6}\right)^{2}-\left(-6^{2}\right)\right)$$

Add 4 and 3 to get 7.

$$|-8.25-\frac{7}{4}|-\left(\left(-6\right)^{3}\left(-\frac{1}{6}\right)^{2}-\left(-6^{2}\right)\right)$$

Convert decimal number -8.25 to fraction -\frac{825}{100}. Reduce the fraction -\frac{825}{100} to lowest terms by extracting and canceling out 25.

$$|-\frac{33}{4}-\frac{7}{4}|-\left(\left(-6\right)^{3}\left(-\frac{1}{6}\right)^{2}-\left(-6^{2}\right)\right)$$

Since -\frac{33}{4} and \frac{7}{4} have the same denominator, subtract them by subtracting their numerators.

$$|\frac{-33-7}{4}|-\left(\left(-6\right)^{3}\left(-\frac{1}{6}\right)^{2}-\left(-6^{2}\right)\right)$$

Subtract 7 from -33 to get -40.

$$|\frac{-40}{4}|-\left(\left(-6\right)^{3}\left(-\frac{1}{6}\right)^{2}-\left(-6^{2}\right)\right)$$

Divide -40 by 4 to get -10.

$$|-10|-\left(\left(-6\right)^{3}\left(-\frac{1}{6}\right)^{2}-\left(-6^{2}\right)\right)$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of -10 is 10.

$$10-\left(\left(-6\right)^{3}\left(-\frac{1}{6}\right)^{2}-\left(-6^{2}\right)\right)$$

Calculate -6 to the power of 3 and get -216.

$$10-\left(-216\left(-\frac{1}{6}\right)^{2}-\left(-6^{2}\right)\right)$$

Calculate -\frac{1}{6} to the power of 2 and get \frac{1}{36}.

$$10-\left(-216\times \frac{1}{36}-\left(-6^{2}\right)\right)$$

Multiply -216 and \frac{1}{36} to get \frac{-216}{36}.

$$10-\left(\frac{-216}{36}-\left(-6^{2}\right)\right)$$

Divide -216 by 36 to get -6.

$$10-\left(-6-\left(-6^{2}\right)\right)$$

Calculate 6 to the power of 2 and get 36.

$$10-\left(-6-\left(-36\right)\right)$$

The opposite of -36 is 36.

$$10-\left(-6+36\right)$$

Add -6 and 36 to get 30.

$$10-30$$

Subtract 30 from 10 to get -20.

$$-20$$

Factor

$$-20$$