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

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

Step 1

Apply the product rule to $\frac{4}{9}$ .

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

Step 2

Simplify the numerator.

Rewrite $4$ as $2^{2}$ .

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Evaluate the exponent.

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

Step 3

Simplify the denominator.

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

$\frac{2}{3^{1}}$

Evaluate the exponent.

$\frac{2}{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{2}{3}$

Decimal Form:

$0.\overline{6}$