Solve 5700{left(1+5.2/12right)}^12*3

$$5700 { \left(1+ \frac{ 5.2 }{ 12 } \right) }^{ 12 \cdot 3 }$$

Evaluate

$$\frac{1212322043113731547487756711795715278839798255776427809574819}{500315450989997070000000000000000000000000000000000}\approx 2423115337.962988076$$

Solution Steps

Expand \frac{5.2}{12} by multiplying both numerator and the denominator by 10.

$$5700\left(1+\frac{52}{120}\right)^{12\times 3}$$

Reduce the fraction \frac{52}{120} to lowest terms by extracting and canceling out 4.

$$5700\left(1+\frac{13}{30}\right)^{12\times 3}$$

Add 1 and \frac{13}{30} to get \frac{43}{30}.

$$5700\times \left(\frac{43}{30}\right)^{12\times 3}$$

Multiply 12 and 3 to get 36.

$$5700\times \left(\frac{43}{30}\right)^{36}$$

Calculate \frac{43}{30} to the power of 36 and get \frac{63806423321775344604618774305037646254726223988233042609201}{150094635296999121000000000000000000000000000000000000}.

$$5700\times \frac{63806423321775344604618774305037646254726223988233042609201}{150094635296999121000000000000000000000000000000000000}$$

Multiply 5700 and \frac{63806423321775344604618774305037646254726223988233042609201}{150094635296999121000000000000000000000000000000000000} to get \frac{1212322043113731547487756711795715278839798255776427809574819}{500315450989997070000000000000000000000000000000000}.

$$\frac{1212322043113731547487756711795715278839798255776427809574819}{500315450989997070000000000000000000000000000000000}$$

Factor

$$\frac{19 \cdot 43 ^ {36}}{2 ^ {34} \cdot 3 ^ {35} \cdot 5 ^ {34}} = 2423115337\frac{4.817979094014983 \times 10^{50}}{5.00315450989997 \times 10^{50}} = 2423115337.9629884$$