Solve 5^{3}*[2^{2}+2^{2}*(3+2^{5}:2^{2}-2*3)-5^{2}+1]^2+(15^2-5^2+6^0):2

$$5 ^ { 3 } \cdot [ 2 ^ { 2 } + 2 ^ { 2 } \times ( 3 + 2 ^ { 5 } : 2 ^ { 2 } - 2 \times 3 ) - 5 ^ { 2 } + 1 ] ^ { 2 } + ( 15 ^ { 2 } - 5 ^ { 2 } + 6 ^ { 0 } ) : 2$$

Evaluate

$$\frac{201}{2}=100.5$$

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.

$$5^{3}\left(2^{2}+2^{2}\left(3+2^{3}-2\times 3\right)-5^{2}+1\right)^{2}+\frac{15^{2}-5^{2}+6^{0}}{2}$$

Calculate 5 to the power of 3 and get 125.

$$125\left(2^{2}+2^{2}\left(3+2^{3}-2\times 3\right)-5^{2}+1\right)^{2}+\frac{15^{2}-5^{2}+6^{0}}{2}$$

Calculate 2 to the power of 2 and get 4.

$$125\left(4+2^{2}\left(3+2^{3}-2\times 3\right)-5^{2}+1\right)^{2}+\frac{15^{2}-5^{2}+6^{0}}{2}$$

Calculate 2 to the power of 2 and get 4.

$$125\left(4+4\left(3+2^{3}-2\times 3\right)-5^{2}+1\right)^{2}+\frac{15^{2}-5^{2}+6^{0}}{2}$$

Calculate 2 to the power of 3 and get 8.

$$125\left(4+4\left(3+8-2\times 3\right)-5^{2}+1\right)^{2}+\frac{15^{2}-5^{2}+6^{0}}{2}$$

Add 3 and 8 to get 11.

$$125\left(4+4\left(11-2\times 3\right)-5^{2}+1\right)^{2}+\frac{15^{2}-5^{2}+6^{0}}{2}$$

Multiply 2 and 3 to get 6.

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

Subtract 6 from 11 to get 5.

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

Multiply 4 and 5 to get 20.

$$125\left(4+20-5^{2}+1\right)^{2}+\frac{15^{2}-5^{2}+6^{0}}{2}$$

Add 4 and 20 to get 24.

$$125\left(24-5^{2}+1\right)^{2}+\frac{15^{2}-5^{2}+6^{0}}{2}$$

Calculate 5 to the power of 2 and get 25.

$$125\left(24-25+1\right)^{2}+\frac{15^{2}-5^{2}+6^{0}}{2}$$

Subtract 25 from 24 to get -1.

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

Add -1 and 1 to get 0.

$$125\times 0^{2}+\frac{15^{2}-5^{2}+6^{0}}{2}$$

Calculate 0 to the power of 2 and get 0.

$$125\times 0+\frac{15^{2}-5^{2}+6^{0}}{2}$$

Multiply 125 and 0 to get 0.

$$0+\frac{15^{2}-5^{2}+6^{0}}{2}$$

Calculate 15 to the power of 2 and get 225.

$$0+\frac{225-5^{2}+6^{0}}{2}$$

Calculate 5 to the power of 2 and get 25.

$$0+\frac{225-25+6^{0}}{2}$$

Subtract 25 from 225 to get 200.

$$0+\frac{200+6^{0}}{2}$$

Calculate 6 to the power of 0 and get 1.

$$0+\frac{200+1}{2}$$

Add 200 and 1 to get 201.

$$0+\frac{201}{2}$$

Add 0 and \frac{201}{2} to get \frac{201}{2}.

$$\frac{201}{2}$$

Factor

$$\frac{3 \cdot 67}{2} = 100\frac{1}{2} = 100.5$$