Solve [(1+3+5)^{2}+5^3/(11)^2-10^2+15]^7+8

$$[ ( 1 + 3 + 5 ) ^ { 2 } + \frac { 5 ^ { 3 } } { ( 11 ) ^ { 2 } } - 10 ^ { 2 } + 15 ] ^ { 7 } + 8$$

Evaluate

$$-\frac{765492558673574991}{379749833583241}\approx -2015.781156375$$

Solution Steps

Add 1 and 3 to get 4.

$$\left(\left(4+5\right)^{2}+\frac{5^{3}}{11^{2}}-10^{2}+15\right)^{7}+8$$

Add 4 and 5 to get 9.

$$\left(9^{2}+\frac{5^{3}}{11^{2}}-10^{2}+15\right)^{7}+8$$

Calculate 9 to the power of 2 and get 81.

$$\left(81+\frac{5^{3}}{11^{2}}-10^{2}+15\right)^{7}+8$$

Calculate 5 to the power of 3 and get 125.

$$\left(81+\frac{125}{11^{2}}-10^{2}+15\right)^{7}+8$$

Calculate 11 to the power of 2 and get 121.

$$\left(81+\frac{125}{121}-10^{2}+15\right)^{7}+8$$

Add 81 and \frac{125}{121} to get \frac{9926}{121}.

$$\left(\frac{9926}{121}-10^{2}+15\right)^{7}+8$$

Calculate 10 to the power of 2 and get 100.

$$\left(\frac{9926}{121}-100+15\right)^{7}+8$$

Subtract 100 from \frac{9926}{121} to get -\frac{2174}{121}.

$$\left(-\frac{2174}{121}+15\right)^{7}+8$$

Add -\frac{2174}{121} and 15 to get -\frac{359}{121}.

$$\left(-\frac{359}{121}\right)^{7}+8$$

Calculate -\frac{359}{121} to the power of 7 and get -\frac{768530557342240919}{379749833583241}.

$$-\frac{768530557342240919}{379749833583241}+8$$

Add -\frac{768530557342240919}{379749833583241} and 8 to get -\frac{765492558673574991}{379749833583241}.

$$-\frac{765492558673574991}{379749833583241}$$

Factor

$$-\frac{765492558673574991}{379749833583241} = -2015\frac{296644003344425}{379749833583241} = -2015.7811563748307$$