Solve 3^{3}+(-3)^{20}:(-3)^{18}*3+3*3^{8}:(-3)^{6}+(-3)^10:(8*3^5+3^5)-2*(-3)^3

$$3 ^ { 3 } + ( - 3 ) ^ { 20 } : ( - 3 ) ^ { 18 } \cdot 3 + 3 \cdot 3 ^ { 8 } : ( - 3 ) ^ { 6 } + ( - 3 ) ^ { 10 } : ( 8 \cdot 3 ^ { 5 } + 3 ^ { 5 } ) - 2 \cdot ( - 3 ) ^ { 3 }$$

Evaluate

$$162$$

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.

$$3^{3}+\left(-3\right)^{2}\times 3+\frac{3\times 3^{8}}{\left(-3\right)^{6}}+\frac{\left(-3\right)^{10}}{8\times 3^{5}+3^{5}}-2\left(-3\right)^{3}$$

To multiply powers of the same base, add their exponents. Add 1 and 8 to get 9.

$$3^{3}+\left(-3\right)^{2}\times 3+\frac{3^{9}}{\left(-3\right)^{6}}+\frac{\left(-3\right)^{10}}{8\times 3^{5}+3^{5}}-2\left(-3\right)^{3}$$

Calculate 3 to the power of 3 and get 27.

$$27+\left(-3\right)^{2}\times 3+\frac{3^{9}}{\left(-3\right)^{6}}+\frac{\left(-3\right)^{10}}{8\times 3^{5}+3^{5}}-2\left(-3\right)^{3}$$

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

$$27+9\times 3+\frac{3^{9}}{\left(-3\right)^{6}}+\frac{\left(-3\right)^{10}}{8\times 3^{5}+3^{5}}-2\left(-3\right)^{3}$$

Multiply 9 and 3 to get 27.

$$27+27+\frac{3^{9}}{\left(-3\right)^{6}}+\frac{\left(-3\right)^{10}}{8\times 3^{5}+3^{5}}-2\left(-3\right)^{3}$$

Add 27 and 27 to get 54.

$$54+\frac{3^{9}}{\left(-3\right)^{6}}+\frac{\left(-3\right)^{10}}{8\times 3^{5}+3^{5}}-2\left(-3\right)^{3}$$

Calculate 3 to the power of 9 and get 19683.

$$54+\frac{19683}{\left(-3\right)^{6}}+\frac{\left(-3\right)^{10}}{8\times 3^{5}+3^{5}}-2\left(-3\right)^{3}$$

Calculate -3 to the power of 6 and get 729.

$$54+\frac{19683}{729}+\frac{\left(-3\right)^{10}}{8\times 3^{5}+3^{5}}-2\left(-3\right)^{3}$$

Divide 19683 by 729 to get 27.

$$54+27+\frac{\left(-3\right)^{10}}{8\times 3^{5}+3^{5}}-2\left(-3\right)^{3}$$

Add 54 and 27 to get 81.

$$81+\frac{\left(-3\right)^{10}}{8\times 3^{5}+3^{5}}-2\left(-3\right)^{3}$$

Calculate -3 to the power of 10 and get 59049.

$$81+\frac{59049}{8\times 3^{5}+3^{5}}-2\left(-3\right)^{3}$$

Calculate 3 to the power of 5 and get 243.

$$81+\frac{59049}{8\times 243+3^{5}}-2\left(-3\right)^{3}$$

Multiply 8 and 243 to get 1944.

$$81+\frac{59049}{1944+3^{5}}-2\left(-3\right)^{3}$$

Calculate 3 to the power of 5 and get 243.

$$81+\frac{59049}{1944+243}-2\left(-3\right)^{3}$$

Add 1944 and 243 to get 2187.

$$81+\frac{59049}{2187}-2\left(-3\right)^{3}$$

Divide 59049 by 2187 to get 27.

$$81+27-2\left(-3\right)^{3}$$

Add 81 and 27 to get 108.

$$108-2\left(-3\right)^{3}$$

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

$$108-2\left(-27\right)$$

Multiply 2 and -27 to get -54.

$$108-\left(-54\right)$$

The opposite of -54 is 54.

$$108+54$$

Add 108 and 54 to get 162.

$$162$$

Factor

$$2\times 3^{4}$$