Simplify (25^(1/2))/(27^(1/3))

$\frac{25^{\frac{1}{2}}}{27^{\frac{1}{3}}}$

Step 1

Simplify the numerator.

Rewrite $25$ as $5^{2}$ .

$\frac{{(5^{2})}^{\frac{1}{2}}}{27^{\frac{1}{3}}}$

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

$\frac{5^{2 (\frac{1}{2})}}{27^{\frac{1}{3}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{5^{2 (\frac{1}{2})}}{27^{\frac{1}{3}}}$

Rewrite the expression.

$\frac{5^{1}}{27^{\frac{1}{3}}}$

Evaluate the exponent.

$\frac{5}{27^{\frac{1}{3}}}$

Step 2

Simplify the denominator.

Rewrite $27$ as $3^{3}$ .

$\frac{5}{{(3^{3})}^{\frac{1}{3}}}$

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

$\frac{5}{3^{3 (\frac{1}{3})}}$

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{5}{3^{3 (\frac{1}{3})}}$

Rewrite the expression.

$\frac{5}{3^{1}}$

Evaluate the exponent.

$\frac{5}{3}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{5}{3}$

Decimal Form:

$1.\overline{6}$

Mixed Number Form:

$1 \frac{2}{3}$