Simplify a^(1/3)+2/(a^(2/3))

$a^{\frac{1}{3}} + \frac{2}{a^{\frac{2}{3}}}$

Step 1

To write $a^{\frac{1}{3}}$ as a fraction with a common denominator, multiply by $\frac{a^{\frac{2}{3}}}{a^{\frac{2}{3}}}$ .

$\frac{a^{\frac{1}{3}} a^{\frac{2}{3}}}{a^{\frac{2}{3}}} + \frac{2}{a^{\frac{2}{3}}}$

Step 2

Combine the numerators over the common denominator.

$\frac{a^{\frac{1}{3}} a^{\frac{2}{3}} + 2}{a^{\frac{2}{3}}}$

Step 3

Simplify the numerator.

Multiply $a^{\frac{1}{3}}$ by $a^{\frac{2}{3}}$ by adding the exponents.

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

$\frac{a^{\frac{1}{3} + \frac{2}{3}} + 2}{a^{\frac{2}{3}}}$

Combine the numerators over the common denominator.

$\frac{a^{\frac{1 + 2}{3}} + 2}{a^{\frac{2}{3}}}$

Add $1$ and $2$ .

$\frac{a^{\frac{3}{3}} + 2}{a^{\frac{2}{3}}}$

Divide $3$ by $3$ .

$\frac{a^{1} + 2}{a^{\frac{2}{3}}}$

Simplify $a^{1}$ .

$\frac{a + 2}{a^{\frac{2}{3}}}$