Solve {left(902/3right)}^12*{left(902/3right)}^6div{left(902/3right)}^2

$${ \left( \frac{ 902 }{ 3 } \right) }^{ 12 } \times { \left( \frac{ 902 }{ 3 } \right) }^{ 6 } \div { \left( \frac{ 902 }{ 3 } \right) }^{ 2 }$$

Evaluate

$$\frac{192001490740278335011133631883088195047076724736}{43046721}\approx 4.460304671 \cdot 10^{39}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 12 and 6 to get 18.

$$\frac{\left(\frac{902}{3}\right)^{18}}{\left(\frac{902}{3}\right)^{2}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 2 from 18 to get 16.

$$\left(\frac{902}{3}\right)^{16}$$

Calculate \frac{902}{3} to the power of 16 and get \frac{192001490740278335011133631883088195047076724736}{43046721}.

$$\frac{192001490740278335011133631883088195047076724736}{43046721}$$

Factor

$$\frac{2 ^ {16} \cdot 11 ^ {16} \cdot 41 ^ {16}}{3 ^ {16}} = 4.4603046708314515 \times 10^{39}\frac{9376648}{43046721} = 4.4603046708314515 \times 10^{39}$$