Evaluate ((5^4)/(3^6))^(1/2)

${(\frac{5^{4}}{3^{6}})}^{\frac{1}{2}}$

Step 1

Simplify the expression.

Raise $5$ to the power of $4$ .

${(\frac{625}{3^{6}})}^{\frac{1}{2}}$

Raise $3$ to the power of $6$ .

${(\frac{625}{729})}^{\frac{1}{2}}$

Apply the product rule to $\frac{625}{729}$ .

$\frac{625^{\frac{1}{2}}}{729^{\frac{1}{2}}}$

Step 2

Simplify the numerator.

Rewrite $625$ as $25^{2}$ .

$\frac{{(25^{2})}^{\frac{1}{2}}}{729^{\frac{1}{2}}}$

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

$\frac{25^{2 (\frac{1}{2})}}{729^{\frac{1}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{25^{2 (\frac{1}{2})}}{729^{\frac{1}{2}}}$

Rewrite the expression.

$\frac{25^{1}}{729^{\frac{1}{2}}}$

Evaluate the exponent.

$\frac{25}{729^{\frac{1}{2}}}$

Step 3

Simplify the denominator.

Rewrite $729$ as $27^{2}$ .

$\frac{25}{{(27^{2})}^{\frac{1}{2}}}$

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

$\frac{25}{27^{2 (\frac{1}{2})}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{25}{27^{2 (\frac{1}{2})}}$

Rewrite the expression.

$\frac{25}{27^{1}}$

Evaluate the exponent.

$\frac{25}{27}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{25}{27}$

Decimal Form:

$0.\overline{925}$