Basic Math Examples

$3^{n + 2} \cdot 9^{n} \div 27^{n}$

Step 1

Rewrite the division as a fraction.

$\frac{3^{n + 2} \cdot 9^{n}}{27^{n}}$

Step 2

Simplify the numerator.

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Step 2.1

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

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

Step 2.2

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

$\frac{3^{n + 2} \cdot 3^{2 n}}{27^{n}}$

Step 2.3

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

$\frac{3^{n + 2 + 2 n}}{27^{n}}$

Step 2.4

Add $n$ and $2 n$ .

$\frac{3^{3 n + 2}}{27^{n}}$