Solve 1000left(252*276-224*276right)^22/500*500*(252+276)*(224+248)

$$\frac{ 1000 { \left(252 \times 276-224 \times 276 \right) }^{ 22 } }{ 500 \times 500 \times (252+276) \times (224+248) }$$

Evaluate

$$\frac{44886451638385563316117878557832675170206236151426729046010825162114855291309785088}{81125}\approx 5.532998661 \cdot 10^{77}$$

Solution Steps

Cancel out 2\times 500 in both numerator and denominator.

$$\frac{\left(252\times 276-224\times 276\right)^{22}}{250\left(224+248\right)\left(252+276\right)}$$

Multiply 252 and 276 to get 69552.

$$\frac{\left(69552-224\times 276\right)^{22}}{250\left(224+248\right)\left(252+276\right)}$$

Multiply 224 and 276 to get 61824.

$$\frac{\left(69552-61824\right)^{22}}{250\left(224+248\right)\left(252+276\right)}$$

Subtract 61824 from 69552 to get 7728.

$$\frac{7728^{22}}{250\left(224+248\right)\left(252+276\right)}$$

Calculate 7728 to the power of 22 and get 34472794858280112626778530732415494530718389364295727907336313724504208863725914947584.

$$\frac{34472794858280112626778530732415494530718389364295727907336313724504208863725914947584}{250\left(224+248\right)\left(252+276\right)}$$

Add 224 and 248 to get 472.

$$\frac{34472794858280112626778530732415494530718389364295727907336313724504208863725914947584}{250\times 472\left(252+276\right)}$$

Multiply 250 and 472 to get 118000.

$$\frac{34472794858280112626778530732415494530718389364295727907336313724504208863725914947584}{118000\left(252+276\right)}$$

Add 252 and 276 to get 528.

$$\frac{34472794858280112626778530732415494530718389364295727907336313724504208863725914947584}{118000\times 528}$$

Multiply 118000 and 528 to get 62304000.

$$\frac{34472794858280112626778530732415494530718389364295727907336313724504208863725914947584}{62304000}$$

Reduce the fraction \frac{34472794858280112626778530732415494530718389364295727907336313724504208863725914947584}{62304000} to lowest terms by extracting and canceling out 768.

$$\frac{44886451638385563316117878557832675170206236151426729046010825162114855291309785088}{81125}$$

Factor

$$\frac{2 ^ {80} \cdot 3 ^ {21} \cdot 7 ^ {22} \cdot 23 ^ {22}}{5 ^ {3} \cdot 11 \cdot 59} = 5.53299866112611 \times 10^{77}\frac{50266}{81125} = 5.53299866112611 \times 10^{77}$$