Solve [(3^{7}:3^{5}+1)+(5^{6}:5^{4})]:[(6^2+13):(3^2-2)]+[(2^4+4):(2^2+1)]

$$[ ( 3 ^ { 7 } : 3 ^ { 5 } + 1 ) + ( 5 ^ { 6 } : 5 ^ { 4 } ) ] : [ ( 6 ^ { 2 } + 13 ) : ( 3 ^ { 2 } - 2 ) ] + [ ( 2 ^ { 4 } + 4 ) : ( 2 ^ { 2 } + 1 ) ]$$

Evaluate

$$9$$

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.

$$\frac{3^{2}+1+\frac{5^{6}}{5^{4}}}{\frac{6^{2}+13}{3^{2}-2}}+\frac{2^{4}+4}{2^{2}+1}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 4 from 6 to get 2.

$$\frac{3^{2}+1+5^{2}}{\frac{6^{2}+13}{3^{2}-2}}+\frac{2^{4}+4}{2^{2}+1}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{9+1+5^{2}}{\frac{6^{2}+13}{3^{2}-2}}+\frac{2^{4}+4}{2^{2}+1}$$

Add 9 and 1 to get 10.

$$\frac{10+5^{2}}{\frac{6^{2}+13}{3^{2}-2}}+\frac{2^{4}+4}{2^{2}+1}$$

Calculate 5 to the power of 2 and get 25.

$$\frac{10+25}{\frac{6^{2}+13}{3^{2}-2}}+\frac{2^{4}+4}{2^{2}+1}$$

Add 10 and 25 to get 35.

$$\frac{35}{\frac{6^{2}+13}{3^{2}-2}}+\frac{2^{4}+4}{2^{2}+1}$$

Calculate 6 to the power of 2 and get 36.

$$\frac{35}{\frac{36+13}{3^{2}-2}}+\frac{2^{4}+4}{2^{2}+1}$$

Add 36 and 13 to get 49.

$$\frac{35}{\frac{49}{3^{2}-2}}+\frac{2^{4}+4}{2^{2}+1}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{35}{\frac{49}{9-2}}+\frac{2^{4}+4}{2^{2}+1}$$

Subtract 2 from 9 to get 7.

$$\frac{35}{\frac{49}{7}}+\frac{2^{4}+4}{2^{2}+1}$$

Divide 49 by 7 to get 7.

$$\frac{35}{7}+\frac{2^{4}+4}{2^{2}+1}$$

Divide 35 by 7 to get 5.

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

Calculate 2 to the power of 4 and get 16.

$$5+\frac{16+4}{2^{2}+1}$$

Add 16 and 4 to get 20.

$$5+\frac{20}{2^{2}+1}$$

Calculate 2 to the power of 2 and get 4.

$$5+\frac{20}{4+1}$$

Add 4 and 1 to get 5.

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

Divide 20 by 5 to get 4.

$$5+4$$

Add 5 and 4 to get 9.

$$9$$

Factor

$$3^{2}$$