Solve (25/9)^35:(5/9)^35

$$( \frac { 25 } { 9 } ) ^ { 35 } : ( \frac { 5 } { 9 } ) ^ { 35 }$$

Evaluate

$$2910383045673370361328125$$

Solution Steps

Calculate \frac{25}{9} to the power of 35 and get \frac{8470329472543003390683225006796419620513916015625}{2503155504993241601315571986085849}.

$$\frac{\frac{8470329472543003390683225006796419620513916015625}{2503155504993241601315571986085849}}{\left(\frac{5}{9}\right)^{35}}$$

Calculate \frac{5}{9} to the power of 35 and get \frac{2910383045673370361328125}{2503155504993241601315571986085849}.

$$\frac{\frac{8470329472543003390683225006796419620513916015625}{2503155504993241601315571986085849}}{\frac{2910383045673370361328125}{2503155504993241601315571986085849}}$$

Divide \frac{8470329472543003390683225006796419620513916015625}{2503155504993241601315571986085849} by \frac{2910383045673370361328125}{2503155504993241601315571986085849} by multiplying \frac{8470329472543003390683225006796419620513916015625}{2503155504993241601315571986085849} by the reciprocal of \frac{2910383045673370361328125}{2503155504993241601315571986085849}.

$$\frac{8470329472543003390683225006796419620513916015625}{2503155504993241601315571986085849}\times \frac{2503155504993241601315571986085849}{2910383045673370361328125}$$

Multiply \frac{8470329472543003390683225006796419620513916015625}{2503155504993241601315571986085849} times \frac{2503155504993241601315571986085849}{2910383045673370361328125} by multiplying numerator times numerator and denominator times denominator.

$$\frac{8470329472543003390683225006796419620513916015625\times 2503155504993241601315571986085849}{2503155504993241601315571986085849\times 2910383045673370361328125}$$

Cancel out 2503155504993241601315571986085849 in both numerator and denominator.

$$\frac{8470329472543003390683225006796419620513916015625}{2910383045673370361328125}$$

Divide 8470329472543003390683225006796419620513916015625 by 2910383045673370361328125 to get 2910383045673370361328125.

$$2910383045673370361328125$$

Factor

$$5^{35}$$