Basic Math Examples

$\frac{{(3 \cdot 3^{3})}^{2}}{3^{6}}$

Step 1

Simplify the numerator.

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Step 1.1

Apply the product rule to $3 \cdot 3^{3}$ .

$\frac{3^{2} \cdot {(3^{3})}^{2}}{3^{6}}$

Step 1.2

Raise $3$ to the power of $2$ .

$\frac{9 \cdot {(3^{3})}^{2}}{3^{6}}$

Step 1.3

Multiply the exponents in ${(3^{3})}^{2}$ .

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Step 1.3.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{9 \cdot 3^{3 \cdot 2}}{3^{6}}$

Step 1.3.2

Multiply $3$ by $2$ .

$\frac{9 \cdot 3^{6}}{3^{6}}$

Step 1.4

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

$\frac{9 \cdot 729}{3^{6}}$

Step 2

Simplify the expression.

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Step 2.1

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

$\frac{9 \cdot 729}{729}$

Step 2.2

Multiply $9$ by $729$ .

$\frac{6561}{729}$

Step 2.3

Divide $6561$ by $729$ .

$9$