Solve [(-1+2^{2})^{3}*3^{5}]^{4}:(-9^6):(5^2+2^1)^3

$$[ ( - 1 + 2 ^ { 2 } ) ^ { 3 } \cdot 3 ^ { 5 } ] ^ { 4 } : ( - 9 ^ { 6 } ) : ( 5 ^ { 2 } + 2 ^ { 1 } ) ^ { 3 }$$

Evaluate

$$-177147$$

Solution Steps

Calculate 2 to the power of 2 and get 4.

$$\frac{\frac{\left(\left(-1+4\right)^{3}\times 3^{5}\right)^{4}}{-9^{6}}}{\left(5^{2}+2^{1}\right)^{3}}$$

Add -1 and 4 to get 3.

$$\frac{\frac{\left(3^{3}\times 3^{5}\right)^{4}}{-9^{6}}}{\left(5^{2}+2^{1}\right)^{3}}$$

Calculate 3 to the power of 3 and get 27.

$$\frac{\frac{\left(27\times 3^{5}\right)^{4}}{-9^{6}}}{\left(5^{2}+2^{1}\right)^{3}}$$

Calculate 3 to the power of 5 and get 243.

$$\frac{\frac{\left(27\times 243\right)^{4}}{-9^{6}}}{\left(5^{2}+2^{1}\right)^{3}}$$

Multiply 27 and 243 to get 6561.

$$\frac{\frac{6561^{4}}{-9^{6}}}{\left(5^{2}+2^{1}\right)^{3}}$$

Calculate 6561 to the power of 4 and get 1853020188851841.

$$\frac{\frac{1853020188851841}{-9^{6}}}{\left(5^{2}+2^{1}\right)^{3}}$$

Calculate 9 to the power of 6 and get 531441.

$$\frac{\frac{1853020188851841}{-531441}}{\left(5^{2}+2^{1}\right)^{3}}$$

Divide 1853020188851841 by -531441 to get -3486784401.

$$\frac{-3486784401}{\left(5^{2}+2^{1}\right)^{3}}$$

Calculate 5 to the power of 2 and get 25.

$$\frac{-3486784401}{\left(25+2^{1}\right)^{3}}$$

Calculate 2 to the power of 1 and get 2.

$$\frac{-3486784401}{\left(25+2\right)^{3}}$$

Add 25 and 2 to get 27.

$$\frac{-3486784401}{27^{3}}$$

Calculate 27 to the power of 3 and get 19683.

$$\frac{-3486784401}{19683}$$

Divide -3486784401 by 19683 to get -177147.

$$-177147$$

Factor

$$-177147$$