Solve {[43-(7^{2}+11^{3}:11^{2}):5+13^0]:2^5+(15-3*2^2)+2^4}:5

$$\{ [ 43 - ( 7 ^ { 2 } + 11 ^ { 3 } : 11 ^ { 2 } ) : 5 + 13 ^ { 0 } ] : 2 ^ { 5 } + ( 15 - 3 \cdot 2 ^ { 2 } ) + 2 ^ { 4 } \} : 5$$

Evaluate

$$4$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 2 from 3 to get 1.

$$\frac{\frac{43-\frac{7^{2}+11^{1}}{5}+13^{0}}{2^{5}}+15-3\times 2^{2}+2^{4}}{5}$$

Calculate 7 to the power of 2 and get 49.

$$\frac{\frac{43-\frac{49+11^{1}}{5}+13^{0}}{2^{5}}+15-3\times 2^{2}+2^{4}}{5}$$

Calculate 11 to the power of 1 and get 11.

$$\frac{\frac{43-\frac{49+11}{5}+13^{0}}{2^{5}}+15-3\times 2^{2}+2^{4}}{5}$$

Add 49 and 11 to get 60.

$$\frac{\frac{43-\frac{60}{5}+13^{0}}{2^{5}}+15-3\times 2^{2}+2^{4}}{5}$$

Divide 60 by 5 to get 12.

$$\frac{\frac{43-12+13^{0}}{2^{5}}+15-3\times 2^{2}+2^{4}}{5}$$

Subtract 12 from 43 to get 31.

$$\frac{\frac{31+13^{0}}{2^{5}}+15-3\times 2^{2}+2^{4}}{5}$$

Calculate 13 to the power of 0 and get 1.

$$\frac{\frac{31+1}{2^{5}}+15-3\times 2^{2}+2^{4}}{5}$$

Add 31 and 1 to get 32.

$$\frac{\frac{32}{2^{5}}+15-3\times 2^{2}+2^{4}}{5}$$

Calculate 2 to the power of 5 and get 32.

$$\frac{\frac{32}{32}+15-3\times 2^{2}+2^{4}}{5}$$

Divide 32 by 32 to get 1.

$$\frac{1+15-3\times 2^{2}+2^{4}}{5}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{1+15-3\times 4+2^{4}}{5}$$

Multiply 3 and 4 to get 12.

$$\frac{1+15-12+2^{4}}{5}$$

Subtract 12 from 15 to get 3.

$$\frac{1+3+2^{4}}{5}$$

Add 1 and 3 to get 4.

$$\frac{4+2^{4}}{5}$$

Calculate 2 to the power of 4 and get 16.

$$\frac{4+16}{5}$$

Add 4 and 16 to get 20.

$$\frac{20}{5}$$

Divide 20 by 5 to get 4.

$$4$$

Factor

$$2^{2}$$