Pre-Algebra Examples

$\frac{3^{5} \cdot 9^{2}}{27}$

Step 1

Simplify the numerator.

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Step 1.1

Rewrite $9$ as $3^{2}$ .

$\frac{3^{5} \cdot {(3^{2})}^{2}}{27}$

Step 1.2

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

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Step 1.2.1

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

$\frac{3^{5} \cdot 3^{2 \cdot 2}}{27}$

Step 1.2.2

Multiply $2$ by $2$ .

$\frac{3^{5} \cdot 3^{4}}{27}$

Step 1.3

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{3^{5 + 4}}{27}$

Step 1.4

Add $5$ and $4$ .

$\frac{3^{9}}{27}$

Step 2

Simplify the expression.

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Step 2.1

Raise $3$ to the power of $9$ .

$\frac{19683}{27}$

Step 2.2

Divide $19683$ by $27$ .

$729$