Solve (-3)^{20}:(-3)^{18}-15:(-3)*(-6)+[(-2)^4]^6:(-2)^23*(-2)^2

$$( - 3 ) ^ { 20 } : ( - 3 ) ^ { 18 } - 15 : ( - 3 ) \cdot ( - 6 ) + [ ( - 2 ) ^ { 4 } ] ^ { 6 } : ( - 2 ) ^ { 23 } \cdot ( - 2 ) ^ { 2 }$$

Evaluate

$$-29$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 18 from 20 to get 2.

$$\left(-3\right)^{2}-\frac{15}{-3}\left(-6\right)+\frac{\left(\left(-2\right)^{4}\right)^{6}}{\left(-2\right)^{23}}\left(-2\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 6 to get 24.

$$\left(-3\right)^{2}-\frac{15}{-3}\left(-6\right)+\frac{\left(-2\right)^{24}}{\left(-2\right)^{23}}\left(-2\right)^{2}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 23 from 24 to get 1.

$$\left(-3\right)^{2}-\frac{15}{-3}\left(-6\right)+\left(-2\right)^{1}\left(-2\right)^{2}$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$\left(-3\right)^{2}-\frac{15}{-3}\left(-6\right)+\left(-2\right)^{3}$$

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

$$9-\frac{15}{-3}\left(-6\right)+\left(-2\right)^{3}$$

Divide 15 by -3 to get -5.

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

Multiply -5 and -6 to get 30.

$$9-30+\left(-2\right)^{3}$$

Subtract 30 from 9 to get -21.

$$-21+\left(-2\right)^{3}$$

Calculate -2 to the power of 3 and get -8.

$$-21-8$$

Subtract 8 from -21 to get -29.

$$-29$$

Factor

$$-29$$