Solve (-3)^{2}-(-3)^{2}-[(-10)^2:(+5)+(-6+4)^5:(-4)^3-3^2]

$$( - 3 ) ^ { 2 } - ( - 3 ) ^ { 2 } - [ ( - 10 ) ^ { 2 } : ( + 5 ) + ( - 6 + 4 ) ^ { 5 } : ( - 4 ) ^ { 3 } - 3 ^ { 2 } ]$$

Evaluate

$$-\frac{23}{2}=-11.5$$

Solution Steps

Calculate -3 to the power of 2 and get 9.

$$9-\left(-3\right)^{2}-\left(\frac{\left(-10\right)^{2}}{5}+\frac{\left(-6+4\right)^{5}}{\left(-4\right)^{3}}-3^{2}\right)$$

Calculate -3 to the power of 2 and get 9.

$$9-9-\left(\frac{\left(-10\right)^{2}}{5}+\frac{\left(-6+4\right)^{5}}{\left(-4\right)^{3}}-3^{2}\right)$$

Subtract 9 from 9 to get 0.

$$0-\left(\frac{\left(-10\right)^{2}}{5}+\frac{\left(-6+4\right)^{5}}{\left(-4\right)^{3}}-3^{2}\right)$$

Calculate -10 to the power of 2 and get 100.

$$0-\left(\frac{100}{5}+\frac{\left(-6+4\right)^{5}}{\left(-4\right)^{3}}-3^{2}\right)$$

Divide 100 by 5 to get 20.

$$0-\left(20+\frac{\left(-6+4\right)^{5}}{\left(-4\right)^{3}}-3^{2}\right)$$

Add -6 and 4 to get -2.

$$0-\left(20+\frac{\left(-2\right)^{5}}{\left(-4\right)^{3}}-3^{2}\right)$$

Calculate -2 to the power of 5 and get -32.

$$0-\left(20+\frac{-32}{\left(-4\right)^{3}}-3^{2}\right)$$

Calculate -4 to the power of 3 and get -64.

$$0-\left(20+\frac{-32}{-64}-3^{2}\right)$$

Reduce the fraction \frac{-32}{-64} to lowest terms by extracting and canceling out -32.

$$0-\left(20+\frac{1}{2}-3^{2}\right)$$

Add 20 and \frac{1}{2} to get \frac{41}{2}.

$$0-\left(\frac{41}{2}-3^{2}\right)$$

Calculate 3 to the power of 2 and get 9.

$$0-\left(\frac{41}{2}-9\right)$$

Subtract 9 from \frac{41}{2} to get \frac{23}{2}.

$$0-\frac{23}{2}$$

Subtract \frac{23}{2} from 0 to get -\frac{23}{2}.

$$-\frac{23}{2}$$

Factor

$$-\frac{23}{2} = -11\frac{1}{2} = -11.5$$