Solve sqrt{6^4*81^25/243^20*16}

$$\sqrt { \frac { 6 ^ { 4 } \cdot 81 ^ { 25 } } { 243 ^ { 20 } \cdot 16 } }$$

Evaluate

$$9$$

Solution Steps

Calculate 6 to the power of 4 and get 1296.

$$\sqrt{\frac{1296\times 81^{25}}{243^{20}\times 16}}$$

Calculate 81 to the power of 25 and get 515377520732011331036461129765621272702107522001.

$$\sqrt{\frac{1296\times 515377520732011331036461129765621272702107522001}{243^{20}\times 16}}$$

Multiply 1296 and 515377520732011331036461129765621272702107522001 to get 667929266868686685023253624176245169421931348513296.

$$\sqrt{\frac{667929266868686685023253624176245169421931348513296}{243^{20}\times 16}}$$

Calculate 243 to the power of 20 and get 515377520732011331036461129765621272702107522001.

$$\sqrt{\frac{667929266868686685023253624176245169421931348513296}{515377520732011331036461129765621272702107522001\times 16}}$$

Multiply 515377520732011331036461129765621272702107522001 and 16 to get 8246040331712181296583378076249940363233720352016.

$$\sqrt{\frac{667929266868686685023253624176245169421931348513296}{8246040331712181296583378076249940363233720352016}}$$

Divide 667929266868686685023253624176245169421931348513296 by 8246040331712181296583378076249940363233720352016 to get 81.

$$\sqrt{81}$$

Calculate the square root of 81 and get 9.

$$9$$

Factor

$$3^{2}$$