Solve (-6+2)^3-80:(-12-4)+(-2)^76:(-2)^72

$$( - 6 + 2 ) ^ { 3 } - 80 : ( - 12 - 4 ) + ( - 2 ) ^ { 76 } : ( - 2 ) ^ { 72 }$$

Evaluate

$$-43$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 72 from 76 to get 4.

$$\left(-6+2\right)^{3}-\frac{80}{-12-4}+\left(-2\right)^{4}$$

Add -6 and 2 to get -4.

$$\left(-4\right)^{3}-\frac{80}{-12-4}+\left(-2\right)^{4}$$

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

$$-64-\frac{80}{-12-4}+\left(-2\right)^{4}$$

Subtract 4 from -12 to get -16.

$$-64-\frac{80}{-16}+\left(-2\right)^{4}$$

Divide 80 by -16 to get -5.

$$-64-\left(-5\right)+\left(-2\right)^{4}$$

The opposite of -5 is 5.

$$-64+5+\left(-2\right)^{4}$$

Add -64 and 5 to get -59.

$$-59+\left(-2\right)^{4}$$

Calculate -2 to the power of 4 and get 16.

$$-59+16$$

Add -59 and 16 to get -43.

$$-43$$

Factor

$$-43$$