Evaluate (4(9)^(1/2))/9

$\frac{4 {(9)}^{\frac{1}{2}}}{9}$

Step 1

Move ${(9)}^{\frac{1}{2}}$ to the denominator using the negative exponent rule $b^{n} = \frac{1}{b^{- n}}$ .

$\frac{4}{9 \cdot 9^{- \frac{1}{2}}}$

Step 2

Multiply $9$ by $9^{- \frac{1}{2}}$ by adding the exponents.

Multiply $9$ by $9^{- \frac{1}{2}}$ .

Raise $9$ to the power of $1$ .

$\frac{4}{9^{1} \cdot 9^{- \frac{1}{2}}}$

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

$\frac{4}{9^{1 - \frac{1}{2}}}$

Write $1$ as a fraction with a common denominator.

$\frac{4}{9^{\frac{2}{2} - \frac{1}{2}}}$

Combine the numerators over the common denominator.

$\frac{4}{9^{\frac{2 - 1}{2}}}$

Subtract $1$ from $2$ .

$\frac{4}{9^{\frac{1}{2}}}$

Step 3

Simplify the denominator.

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

$\frac{4}{{(3^{2})}^{\frac{1}{2}}}$

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

$\frac{4}{3^{2 (\frac{1}{2})}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{4}{3^{2 (\frac{1}{2})}}$

Rewrite the expression.

$\frac{4}{3^{1}}$

Evaluate the exponent.

$\frac{4}{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{4}{3}$

Decimal Form:

$1.\overline{3}$

Mixed Number Form:

$1 \frac{1}{3}$