Algebra Examples

$\frac{81^{\frac{1}{2}}}{9^{\frac{1}{2}}}$

Step 1

Simplify the numerator.

Tap for more steps...

Step 1.1

Rewrite $81$ as $9^{2}$ .

$\frac{{(9^{2})}^{\frac{1}{2}}}{9^{\frac{1}{2}}}$

Step 1.2

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

$\frac{9^{2 (\frac{1}{2})}}{9^{\frac{1}{2}}}$

Step 1.3

Cancel the common factor of $2$ .

Tap for more steps...

Step 1.3.1

Cancel the common factor.

$\frac{9^{2 (\frac{1}{2})}}{9^{\frac{1}{2}}}$

Step 1.3.2

Rewrite the expression.

$\frac{9^{1}}{9^{\frac{1}{2}}}$

Step 1.4

Evaluate the exponent.

$\frac{9}{9^{\frac{1}{2}}}$

Step 2

Simplify the denominator.

Tap for more steps...

Step 2.1

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

$\frac{9}{{(3^{2})}^{\frac{1}{2}}}$

Step 2.2

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

$\frac{9}{3^{2 (\frac{1}{2})}}$

Step 2.3

Cancel the common factor of $2$ .

Tap for more steps...

Step 2.3.1

Cancel the common factor.

$\frac{9}{3^{2 (\frac{1}{2})}}$

Step 2.3.2

Rewrite the expression.

$\frac{9}{3^{1}}$

Step 2.4

Evaluate the exponent.

$\frac{9}{3}$

Step 3

Divide $9$ by $3$ .

$3$