Solve {left(111/25right)}^105^21/6^17

$${ \left(1 \frac{ 11 }{ 25 } \right) }^{ 10 } \frac{ { 5 }^{ 21 } }{ { 6 }^{ 17 } }$$

Evaluate

$$1080$$

Solution Steps

Multiply 1 and 25 to get 25.

$$\left(\frac{25+11}{25}\right)^{10}\times \frac{5^{21}}{6^{17}}$$

Add 25 and 11 to get 36.

$$\left(\frac{36}{25}\right)^{10}\times \frac{5^{21}}{6^{17}}$$

Calculate \frac{36}{25} to the power of 10 and get \frac{3656158440062976}{95367431640625}.

$$\frac{3656158440062976}{95367431640625}\times \frac{5^{21}}{6^{17}}$$

Calculate 5 to the power of 21 and get 476837158203125.

$$\frac{3656158440062976}{95367431640625}\times \frac{476837158203125}{6^{17}}$$

Calculate 6 to the power of 17 and get 16926659444736.

$$\frac{3656158440062976}{95367431640625}\times \frac{476837158203125}{16926659444736}$$

Multiply \frac{3656158440062976}{95367431640625} and \frac{476837158203125}{16926659444736} to get 1080.

$$1080$$

Factor

$$2^{3}\times 3^{3}\times 5$$