Algebra Examples

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

Step 1

Simplify the numerator.

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Step 1.1

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

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

Step 1.2

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

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

Step 1.3

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

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

Step 1.4

Combine exponents.

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Step 1.4.1

Multiply $85766121$ by $42875$ .

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

Step 1.4.2

Multiply $3677222437875$ by $512000$ .

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

Step 2

Simplify the denominator.

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Step 2.1

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

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

Step 2.2

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

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

Step 2.3

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

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

Step 2.4

Combine exponents.

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Step 2.4.1

Multiply $50625$ by $20661046784$ .

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

Step 2.4.2

Multiply $1045965493440000$ by $900$ .

$\frac{1882737888192000000}{941368944096000000}$

Step 3

Divide $1882737888192000000$ by $941368944096000000$ .

$2$