Solve 3^{7}:3^{5}+{5^{4}:5^{2}-3*[7^{2}-5*(3*2^{2}:2^{2}+3^{3}:3^{2})-2^4]}:2^3-7^5:7^4

$$3 ^ { 7 } : 3 ^ { 5 } + \{ 5 ^ { 4 } : 5 ^ { 2 } - 3 \cdot [ 7 ^ { 2 } - 5 \cdot ( 3 \cdot 2 ^ { 2 } : 2 ^ { 2 } + 3 ^ { 3 } : 3 ^ { 2 } ) - 2 ^ { 4 } ] \} : 2 ^ { 3 } - 7 ^ { 5 } : 7 ^ { 4 }$$

Evaluate

$$4$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 5 from 7 to get 2.

$$3^{2}+\frac{\frac{5^{4}}{5^{2}}-3\left(7^{2}-5\left(\frac{3\times 2^{2}}{2^{2}}+\frac{3^{3}}{3^{2}}\right)-2^{4}\right)}{2^{3}}-\frac{7^{5}}{7^{4}}$$

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

$$3^{2}+\frac{5^{2}-3\left(7^{2}-5\left(\frac{3\times 2^{2}}{2^{2}}+\frac{3^{3}}{3^{2}}\right)-2^{4}\right)}{2^{3}}-\frac{7^{5}}{7^{4}}$$

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

$$3^{2}+\frac{5^{2}-3\left(7^{2}-5\left(\frac{3\times 2^{2}}{2^{2}}+3^{1}\right)-2^{4}\right)}{2^{3}}-\frac{7^{5}}{7^{4}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 4 from 5 to get 1.

$$3^{2}+\frac{5^{2}-3\left(7^{2}-5\left(\frac{3\times 2^{2}}{2^{2}}+3^{1}\right)-2^{4}\right)}{2^{3}}-7^{1}$$

Calculate 3 to the power of 2 and get 9.

$$9+\frac{5^{2}-3\left(7^{2}-5\left(\frac{3\times 2^{2}}{2^{2}}+3^{1}\right)-2^{4}\right)}{2^{3}}-7^{1}$$

Calculate 5 to the power of 2 and get 25.

$$9+\frac{25-3\left(7^{2}-5\left(\frac{3\times 2^{2}}{2^{2}}+3^{1}\right)-2^{4}\right)}{2^{3}}-7^{1}$$

Calculate 7 to the power of 2 and get 49.

$$9+\frac{25-3\left(49-5\left(\frac{3\times 2^{2}}{2^{2}}+3^{1}\right)-2^{4}\right)}{2^{3}}-7^{1}$$

Cancel out 2^{2} in both numerator and denominator.

$$9+\frac{25-3\left(49-5\left(3+3^{1}\right)-2^{4}\right)}{2^{3}}-7^{1}$$

Calculate 3 to the power of 1 and get 3.

$$9+\frac{25-3\left(49-5\left(3+3\right)-2^{4}\right)}{2^{3}}-7^{1}$$

Add 3 and 3 to get 6.

$$9+\frac{25-3\left(49-5\times 6-2^{4}\right)}{2^{3}}-7^{1}$$

Multiply 5 and 6 to get 30.

$$9+\frac{25-3\left(49-30-2^{4}\right)}{2^{3}}-7^{1}$$

Subtract 30 from 49 to get 19.

$$9+\frac{25-3\left(19-2^{4}\right)}{2^{3}}-7^{1}$$

Calculate 2 to the power of 4 and get 16.

$$9+\frac{25-3\left(19-16\right)}{2^{3}}-7^{1}$$

Subtract 16 from 19 to get 3.

$$9+\frac{25-3\times 3}{2^{3}}-7^{1}$$

Multiply 3 and 3 to get 9.

$$9+\frac{25-9}{2^{3}}-7^{1}$$

Subtract 9 from 25 to get 16.

$$9+\frac{16}{2^{3}}-7^{1}$$

Calculate 2 to the power of 3 and get 8.

$$9+\frac{16}{8}-7^{1}$$

Divide 16 by 8 to get 2.

$$9+2-7^{1}$$

Add 9 and 2 to get 11.

$$11-7^{1}$$

Calculate 7 to the power of 1 and get 7.

$$11-7$$

Subtract 7 from 11 to get 4.

$$4$$

Factor

$$2^{2}$$