Simplify ( square root of 27)/( square root of 3^3)

$\frac{\sqrt{27}}{\sqrt{3^{3}}}$

Simplify the numerator.

Rewrite $27$ as $3^{2} \cdot 3$ .

Factor $9$ out of $27$ .

$\frac{\sqrt{9 (3)}}{\sqrt{3^{3}}}$

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

$\frac{\sqrt{3^{2} \cdot 3}}{\sqrt{3^{3}}}$

Pull terms out from under the radical.

$\frac{3 \sqrt{3}}{\sqrt{3^{3}}}$

Simplify the denominator.

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

$\frac{3 \sqrt{3}}{\sqrt{27}}$

Rewrite $27$ as $3^{2} \cdot 3$ .

Factor $9$ out of $27$ .

$\frac{3 \sqrt{3}}{\sqrt{9 (3)}}$

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

$\frac{3 \sqrt{3}}{\sqrt{3^{2} \cdot 3}}$

Pull terms out from under the radical.

$\frac{3 \sqrt{3}}{3 \sqrt{3}}$

Reduce the expression by cancelling the common factors.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 \sqrt{3}}{3 \sqrt{3}}$

Rewrite the expression.

$\frac{\sqrt{3}}{\sqrt{3}}$

Cancel the common factor of $\sqrt{3}$ .

Cancel the common factor.

$\frac{\sqrt{3}}{\sqrt{3}}$

Rewrite the expression.

$1$