Solve [5^{0}+(6^{11}:6^{0}+3):(5+2^{3})-(10^4:10^2-3^2*11)]*3+3^2=

$$[ 5 ^ { 0 } + ( 6 ^ { 11 } : 6 ^ { 0 } + 3 ) : ( 5 + 2 ^ { 3 } ) - ( 10 ^ { 4 } : 10 ^ { 2 } - 3 ^ { 2 } \times 11 ) ] \times 3 + 3 ^ { 2 } =$$

Evaluate

$$\frac{1088391294}{13}\approx 83722407.230769231$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 0 from 11 to get 11.

$$\left(5^{0}+\frac{6^{11}+3}{5+2^{3}}-\left(\frac{10^{4}}{10^{2}}-3^{2}\times 11\right)\right)\times 3+3^{2}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 2 from 4 to get 2.

$$\left(5^{0}+\frac{6^{11}+3}{5+2^{3}}-\left(10^{2}-3^{2}\times 11\right)\right)\times 3+3^{2}$$

Calculate 5 to the power of 0 and get 1.

$$\left(1+\frac{6^{11}+3}{5+2^{3}}-\left(10^{2}-3^{2}\times 11\right)\right)\times 3+3^{2}$$

Calculate 6 to the power of 11 and get 362797056.

$$\left(1+\frac{362797056+3}{5+2^{3}}-\left(10^{2}-3^{2}\times 11\right)\right)\times 3+3^{2}$$

Add 362797056 and 3 to get 362797059.

$$\left(1+\frac{362797059}{5+2^{3}}-\left(10^{2}-3^{2}\times 11\right)\right)\times 3+3^{2}$$

Calculate 2 to the power of 3 and get 8.

$$\left(1+\frac{362797059}{5+8}-\left(10^{2}-3^{2}\times 11\right)\right)\times 3+3^{2}$$

Add 5 and 8 to get 13.

$$\left(1+\frac{362797059}{13}-\left(10^{2}-3^{2}\times 11\right)\right)\times 3+3^{2}$$

Add 1 and \frac{362797059}{13} to get \frac{362797072}{13}.

$$\left(\frac{362797072}{13}-\left(10^{2}-3^{2}\times 11\right)\right)\times 3+3^{2}$$

Calculate 10 to the power of 2 and get 100.

$$\left(\frac{362797072}{13}-\left(100-3^{2}\times 11\right)\right)\times 3+3^{2}$$

Calculate 3 to the power of 2 and get 9.

$$\left(\frac{362797072}{13}-\left(100-9\times 11\right)\right)\times 3+3^{2}$$

Multiply 9 and 11 to get 99.

$$\left(\frac{362797072}{13}-\left(100-99\right)\right)\times 3+3^{2}$$

Subtract 99 from 100 to get 1.

$$\left(\frac{362797072}{13}-1\right)\times 3+3^{2}$$

Subtract 1 from \frac{362797072}{13} to get \frac{362797059}{13}.

$$\frac{362797059}{13}\times 3+3^{2}$$

Multiply \frac{362797059}{13} and 3 to get \frac{1088391177}{13}.

$$\frac{1088391177}{13}+3^{2}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{1088391177}{13}+9$$

Add \frac{1088391177}{13} and 9 to get \frac{1088391294}{13}.

$$\frac{1088391294}{13}$$

Factor

$$\frac{2 \cdot 3 ^ {2} \cdot 137 \cdot 441359}{13} = 83722407\frac{3}{13} = 83722407.23076923$$