Simplify (21^635^380^3)/(15^414^930^2)

$\frac{21^{6} \cdot 35^{3} \cdot 80^{3}}{15^{4} \cdot 14^{9} \cdot 30^{2}}$

Step 1

Simplify the numerator.

Raise $21$ to the power of $6$ .

$\frac{85766121 \cdot 35^{3} \cdot 80^{3}}{15^{4} \cdot 14^{9} \cdot 30^{2}}$

Raise $35$ to the power of $3$ .

$\frac{85766121 \cdot 42875 \cdot 80^{3}}{15^{4} \cdot 14^{9} \cdot 30^{2}}$

Raise $80$ to the power of $3$ .

$\frac{85766121 \cdot 42875 \cdot 512000}{15^{4} \cdot 14^{9} \cdot 30^{2}}$

Combine exponents.

Multiply $85766121$ by $42875$ .

$\frac{3677222437875 \cdot 512000}{15^{4} \cdot 14^{9} \cdot 30^{2}}$

Multiply $3677222437875$ by $512000$ .

$\frac{1882737888192000000}{15^{4} \cdot 14^{9} \cdot 30^{2}}$

Step 2

Simplify the denominator.

Raise $15$ to the power of $4$ .

$\frac{1882737888192000000}{50625 \cdot 14^{9} \cdot 30^{2}}$

Raise $14$ to the power of $9$ .

$\frac{1882737888192000000}{50625 \cdot 20661046784 \cdot 30^{2}}$

Raise $30$ to the power of $2$ .

$\frac{1882737888192000000}{50625 \cdot 20661046784 \cdot 900}$

Combine exponents.

Multiply $50625$ by $20661046784$ .

$\frac{1882737888192000000}{1045965493440000 \cdot 900}$

Multiply $1045965493440000$ by $900$ .

$\frac{1882737888192000000}{941368944096000000}$

Step 3

Divide $1882737888192000000$ by $941368944096000000$ .

$2$

Simplify (21^6*35^3*80^3)/(15^4*14^9*30^2)