Algebra Examples

$\frac{54^{3} \cdot 125^{2} \cdot 8^{2}}{6^{3} \cdot 30^{6}}$

Step 1

Simplify the numerator.

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Step 1.1

Raise $54$ to the power of $3$ .

$\frac{157464 \cdot 125^{2} \cdot 8^{2}}{6^{3} \cdot 30^{6}}$

Step 1.2

Raise $125$ to the power of $2$ .

$\frac{157464 \cdot 15625 \cdot 8^{2}}{6^{3} \cdot 30^{6}}$

Step 1.3

Raise $8$ to the power of $2$ .

$\frac{157464 \cdot 15625 \cdot 64}{6^{3} \cdot 30^{6}}$

Step 1.4

Combine exponents.

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Step 1.4.1

Multiply $157464$ by $15625$ .

$\frac{2460375000 \cdot 64}{6^{3} \cdot 30^{6}}$

Step 1.4.2

Multiply $2460375000$ by $64$ .

$\frac{157464000000}{6^{3} \cdot 30^{6}}$

Step 2

Simplify the denominator.

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Step 2.1

Raise $6$ to the power of $3$ .

$\frac{157464000000}{216 \cdot 30^{6}}$

Step 2.2

Raise $30$ to the power of $6$ .

$\frac{157464000000}{216 \cdot 729000000}$

Step 3

Simplify the expression.

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Step 3.1

Multiply $216$ by $729000000$ .

$\frac{157464000000}{157464000000}$

Step 3.2

Divide $157464000000$ by $157464000000$ .

$1$