Evaluate (9/49)^(1/2)

${(\frac{9}{49})}^{\frac{1}{2}}$

Step 1

Apply the product rule to $\frac{9}{49}$ .

$\frac{9^{\frac{1}{2}}}{49^{\frac{1}{2}}}$

Step 2

Simplify the numerator.

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

$\frac{{(3^{2})}^{\frac{1}{2}}}{49^{\frac{1}{2}}}$

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

$\frac{3^{2 (\frac{1}{2})}}{49^{\frac{1}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{3^{2 (\frac{1}{2})}}{49^{\frac{1}{2}}}$

Rewrite the expression.

$\frac{3^{1}}{49^{\frac{1}{2}}}$

Evaluate the exponent.

$\frac{3}{49^{\frac{1}{2}}}$

Step 3

Simplify the denominator.

Rewrite $49$ as $7^{2}$ .

$\frac{3}{{(7^{2})}^{\frac{1}{2}}}$

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

$\frac{3}{7^{2 (\frac{1}{2})}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{3}{7^{2 (\frac{1}{2})}}$

Rewrite the expression.

$\frac{3}{7^{1}}$

Evaluate the exponent.

$\frac{3}{7}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{3}{7}$

Decimal Form:

$0.\overline{428571}$