Solve [(-2)^{2}+(-3)]*(-1)+[(+3)^{3}*(-3)^{6}]:(-3)^9+[(-2)^3]^2:(-2)^4

$$[ ( - 2 ) ^ { 2 } + ( - 3 ) ] \cdot ( - 1 ) + [ ( + 3 ) ^ { 3 } \cdot ( - 3 ) ^ { 6 } ] : ( - 3 ) ^ { 9 } + [ ( - 2 ) ^ { 3 } ] ^ { 2 } : ( - 2 ) ^ { 4 }$$

Evaluate

$$2$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

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

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 4 from 6 to get 2.

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

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

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

Subtract 3 from 4 to get 1.

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

Multiply 1 and -1 to get -1.

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

Cancel out \left(-3\right)^{6} in both numerator and denominator.

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

Calculate 3 to the power of 3 and get 27.

$$-1+\frac{27}{\left(-3\right)^{3}}+\left(-2\right)^{2}$$

Calculate -3 to the power of 3 and get -27.

$$-1+\frac{27}{-27}+\left(-2\right)^{2}$$

Divide 27 by -27 to get -1.

$$-1-1+\left(-2\right)^{2}$$

Subtract 1 from -1 to get -2.

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

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

$$-2+4$$

Add -2 and 4 to get 2.

$$2$$

Factor

$$2$$