Solve frac{(53)^{4}+4+(40)^4}{(5^3)^2+2(44)^2+5194}=?

$$\frac { ( 53 ) ^ { 4 } + 4 + ( 40 ) ^ { 4 } } { ( 5 ^ { 3 } ) ^ { 2 } + 2 ( 44 ) ^ { 2 } + 5194 } = ?$$

Evaluate

$$\frac{10450485}{24691}\approx 423.250779636$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$\frac{53^{4}+4+40^{4}}{5^{6}+2\times 44^{2}+5194}$$

Calculate 53 to the power of 4 and get 7890481.

$$\frac{7890481+4+40^{4}}{5^{6}+2\times 44^{2}+5194}$$

Add 7890481 and 4 to get 7890485.

$$\frac{7890485+40^{4}}{5^{6}+2\times 44^{2}+5194}$$

Calculate 40 to the power of 4 and get 2560000.

$$\frac{7890485+2560000}{5^{6}+2\times 44^{2}+5194}$$

Add 7890485 and 2560000 to get 10450485.

$$\frac{10450485}{5^{6}+2\times 44^{2}+5194}$$

Calculate 5 to the power of 6 and get 15625.

$$\frac{10450485}{15625+2\times 44^{2}+5194}$$

Calculate 44 to the power of 2 and get 1936.

$$\frac{10450485}{15625+2\times 1936+5194}$$

Multiply 2 and 1936 to get 3872.

$$\frac{10450485}{15625+3872+5194}$$

Add 15625 and 3872 to get 19497.

$$\frac{10450485}{19497+5194}$$

Add 19497 and 5194 to get 24691.

$$\frac{10450485}{24691}$$

Factor

$$\frac{3 ^ {3} \cdot 5 \cdot 199 \cdot 389}{24691} = 423\frac{6192}{24691} = 423.25077963630474$$