Simplify cube root of (27t^9)/729

$\sqrt[3]{\frac{27 t^{9}}{729}}$

Step 1

Reduce the expression $\frac{27 t^{9}}{729}$ by cancelling the common factors.

Factor $27$ out of $27 t^{9}$ .

$\sqrt[3]{\frac{27 (t^{9})}{729}}$

Factor $27$ out of $729$ .

$\sqrt[3]{\frac{27 t^{9}}{27 \cdot 27}}$

Cancel the common factor.

$\sqrt[3]{\frac{27 t^{9}}{27 \cdot 27}}$

Rewrite the expression.

$\sqrt[3]{\frac{t^{9}}{27}}$

Step 2

Simplify the expression.

Rewrite $t^{9}$ as ${(t^{3})}^{3}$ .

$\sqrt[3]{\frac{{(t^{3})}^{3}}{27}}$

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

$\sqrt[3]{\frac{{(t^{3})}^{3}}{3^{3}}}$

Step 3

Rewrite $\frac{{(t^{3})}^{3}}{3^{3}}$ as ${(\frac{t^{3}}{3})}^{3}$ .

$\sqrt[3]{{(\frac{t^{3}}{3})}^{3}}$

Step 4

Pull terms out from under the radical, assuming real numbers.

$\frac{t^{3}}{3}$