Solve 5^{3}:[3^{2}+2^{2}*(3+2^{5}:2^{2}-2*3)-5^2+1]^2+(15^2:5^2+0):2

$$5 ^ { 3 } : [ 3 ^ { 2 } + 2 ^ { 2 } \times ( 3 + 2 ^ { 5 } : 2 ^ { 2 } - 2 \times 3 ) - 5 ^ { 2 } + 1 ] ^ { 2 } + ( 15 ^ { 2 } : 5 ^ { 2 } + 0 ) : 2$$

Evaluate

$$\frac{19}{2}=9.5$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 2 from 5 to get 3.

$$\frac{5^{3}}{\left(3^{2}+2^{2}\left(3+2^{3}-2\times 3\right)-5^{2}+1\right)^{2}}+\frac{\frac{15^{2}}{5^{2}}+0}{2}$$

Calculate 5 to the power of 3 and get 125.

$$\frac{125}{\left(3^{2}+2^{2}\left(3+2^{3}-2\times 3\right)-5^{2}+1\right)^{2}}+\frac{\frac{15^{2}}{5^{2}}+0}{2}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{125}{\left(9+2^{2}\left(3+2^{3}-2\times 3\right)-5^{2}+1\right)^{2}}+\frac{\frac{15^{2}}{5^{2}}+0}{2}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{125}{\left(9+4\left(3+2^{3}-2\times 3\right)-5^{2}+1\right)^{2}}+\frac{\frac{15^{2}}{5^{2}}+0}{2}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{125}{\left(9+4\left(3+8-2\times 3\right)-5^{2}+1\right)^{2}}+\frac{\frac{15^{2}}{5^{2}}+0}{2}$$

Add 3 and 8 to get 11.

$$\frac{125}{\left(9+4\left(11-2\times 3\right)-5^{2}+1\right)^{2}}+\frac{\frac{15^{2}}{5^{2}}+0}{2}$$

Multiply 2 and 3 to get 6.

$$\frac{125}{\left(9+4\left(11-6\right)-5^{2}+1\right)^{2}}+\frac{\frac{15^{2}}{5^{2}}+0}{2}$$

Subtract 6 from 11 to get 5.

$$\frac{125}{\left(9+4\times 5-5^{2}+1\right)^{2}}+\frac{\frac{15^{2}}{5^{2}}+0}{2}$$

Multiply 4 and 5 to get 20.

$$\frac{125}{\left(9+20-5^{2}+1\right)^{2}}+\frac{\frac{15^{2}}{5^{2}}+0}{2}$$

Add 9 and 20 to get 29.

$$\frac{125}{\left(29-5^{2}+1\right)^{2}}+\frac{\frac{15^{2}}{5^{2}}+0}{2}$$

Calculate 5 to the power of 2 and get 25.

$$\frac{125}{\left(29-25+1\right)^{2}}+\frac{\frac{15^{2}}{5^{2}}+0}{2}$$

Subtract 25 from 29 to get 4.

$$\frac{125}{\left(4+1\right)^{2}}+\frac{\frac{15^{2}}{5^{2}}+0}{2}$$

Add 4 and 1 to get 5.

$$\frac{125}{5^{2}}+\frac{\frac{15^{2}}{5^{2}}+0}{2}$$

Calculate 5 to the power of 2 and get 25.

$$\frac{125}{25}+\frac{\frac{15^{2}}{5^{2}}+0}{2}$$

Divide 125 by 25 to get 5.

$$5+\frac{\frac{15^{2}}{5^{2}}+0}{2}$$

Calculate 15 to the power of 2 and get 225.

$$5+\frac{\frac{225}{5^{2}}+0}{2}$$

Calculate 5 to the power of 2 and get 25.

$$5+\frac{\frac{225}{25}+0}{2}$$

Divide 225 by 25 to get 9.

$$5+\frac{9+0}{2}$$

Add 9 and 0 to get 9.

$$5+\frac{9}{2}$$

Add 5 and \frac{9}{2} to get \frac{19}{2}.

$$\frac{19}{2}$$

Factor

$$\frac{19}{2} = 9\frac{1}{2} = 9.5$$