Trigonometry Examples

$\frac{81^{5} \cdot 3^{- 3}}{9^{5}}$

Step 1

Move $3^{- 3}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{81^{5}}{9^{5} \cdot 3^{3}}$

Step 2

Simplify the denominator.

Tap for more steps...

Step 2.1

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

$\frac{81^{5}}{{(3^{2})}^{5} \cdot 3^{3}}$

Step 2.2

Multiply the exponents in ${(3^{2})}^{5}$ .

Tap for more steps...

Step 2.2.1

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

$\frac{81^{5}}{3^{2 \cdot 5} \cdot 3^{3}}$

Step 2.2.2

Multiply $2$ by $5$ .

$\frac{81^{5}}{3^{10} \cdot 3^{3}}$

Step 2.3

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

$\frac{81^{5}}{3^{10 + 3}}$

Step 2.4

Add $10$ and $3$ .

$\frac{81^{5}}{3^{13}}$

Step 3

Raise $81$ to the power of $5$ .

$\frac{3486784401}{3^{13}}$

Step 4

Raise $3$ to the power of $13$ .

$\frac{3486784401}{1594323}$

Step 5

Divide $3486784401$ by $1594323$ .

$2187$