Question

which expression is equivalent to $x^{2/3}+\frac{1}{x^{2/3}}$?\
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a $\frac{x^{2/3}+1}{x^{2/3}}$\
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b $\frac{x^{4/9}+1}{x^{2/3}}$\
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c 1\
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d $\frac{x + 1}{x^{2/3}}$\
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e $\frac{x^{4/3}+1}{x^{2/3}}$

Explanation:

Step1: Rewrite to common denominator

To add the terms, rewrite $x^{2/3}$ with denominator $x^{2/3}$ using exponent rule $x^a \cdot x^a = x^{2a}$.
$x^{2/3} = \frac{x^{2/3} \cdot x^{2/3}}{x^{2/3}} = \frac{x^{4/3}}{x^{2/3}}$

Step2: Add the fractions

Combine the two fractions over the common denominator.
$\frac{x^{4/3}}{x^{2/3}} + \frac{1}{x^{2/3}} = \frac{x^{4/3} + 1}{x^{2/3}}$

Answer:

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