Solve -3^2+(-0.25)^100*4^100+(1/2-1/3)*(1/6)^-2

$$- 3 ^ { 2 } + ( - 0.25 ) ^ { 100 } \times 4 ^ { 100 } + ( \frac { 1 } { 2 } - \frac { 1 } { 3 } ) \times ( \frac { 1 } { 6 } ) ^ { - 2 }$$

Evaluate

$$-2$$

Solution Steps

Calculate 3 to the power of 2 and get 9.

$$-9+\left(-0.25\right)^{100}\times 4^{100}+\left(\frac{1}{2}-\frac{1}{3}\right)\times \left(\frac{1}{6}\right)^{-2}$$

Calculate -0.25 to the power of 100 and get 0.00000000000000000000000000000000000000000000000000000000000062230152778611417071440640537801242405902521687211671331011166147896988340353834411839448231257136169569665895551224821247160434722900390625.

$$-9+0.00000000000000000000000000000000000000000000000000000000000062230152778611417071440640537801242405902521687211671331011166147896988340353834411839448231257136169569665895551224821247160434722900390625\times 4^{100}+\left(\frac{1}{2}-\frac{1}{3}\right)\times \left(\frac{1}{6}\right)^{-2}$$

Calculate 4 to the power of 100 and get 1606938044258990275541962092341162602522202993782792835301376.

$$-9+0.00000000000000000000000000000000000000000000000000000000000062230152778611417071440640537801242405902521687211671331011166147896988340353834411839448231257136169569665895551224821247160434722900390625\times 1606938044258990275541962092341162602522202993782792835301376+\left(\frac{1}{2}-\frac{1}{3}\right)\times \left(\frac{1}{6}\right)^{-2}$$

Multiply 0.00000000000000000000000000000000000000000000000000000000000062230152778611417071440640537801242405902521687211671331011166147896988340353834411839448231257136169569665895551224821247160434722900390625 and 1606938044258990275541962092341162602522202993782792835301376 to get 1.

$$-9+1+\left(\frac{1}{2}-\frac{1}{3}\right)\times \left(\frac{1}{6}\right)^{-2}$$

Add -9 and 1 to get -8.

$$-8+\left(\frac{1}{2}-\frac{1}{3}\right)\times \left(\frac{1}{6}\right)^{-2}$$

Subtract \frac{1}{3} from \frac{1}{2} to get \frac{1}{6}.

$$-8+\frac{1}{6}\times \left(\frac{1}{6}\right)^{-2}$$

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

$$-8+\frac{1}{6}\times 36$$

Multiply \frac{1}{6} and 36 to get 6.

$$-8+6$$

Add -8 and 6 to get -2.

$$-2$$

Factor

$$-2$$