Simplify cube root of t square root of t

$\sqrt[3]{t} \sqrt{t}$

Step 1

Rewrite the expression using the least common index of $6$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{t}$ as $t^{\frac{1}{3}}$ .

$t^{\frac{1}{3}} \sqrt{t}$

Rewrite $t^{\frac{1}{3}}$ as $t^{\frac{2}{6}}$ .

$t^{\frac{2}{6}} \sqrt{t}$

Rewrite $t^{\frac{2}{6}}$ as $\sqrt[6]{t^{2}}$ .

$\sqrt[6]{t^{2}} \sqrt{t}$

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{t}$ as $t^{\frac{1}{2}}$ .

$\sqrt[6]{t^{2}} t^{\frac{1}{2}}$

Rewrite $t^{\frac{1}{2}}$ as $t^{\frac{3}{6}}$ .

$\sqrt[6]{t^{2}} t^{\frac{3}{6}}$

Rewrite $t^{\frac{3}{6}}$ as $\sqrt[6]{t^{3}}$ .

$\sqrt[6]{t^{2}} \sqrt[6]{t^{3}}$

Step 2

Combine using the product rule for radicals.

$\sqrt[6]{t^{2} t^{3}}$

Step 3

Multiply $t^{2}$ by $t^{3}$ by adding the exponents.

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\sqrt[6]{t^{2 + 3}}$

Add $2$ and $3$ .

$\sqrt[6]{t^{5}}$