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

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

Step 1

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

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

Step 2

Combine the numerators over the common denominator.

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

Step 3

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

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

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

Combine the numerators over the common denominator.

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

Add $2$ and $2$ .

$\frac{x^{\frac{4}{3}} + 1}{x^{\frac{2}{3}}}$