Question

evaluate the left hand side to find the value of a in the equation in simplest form.
$x^{\frac{2}{3}}x^{\frac{1}{2}} = x^{a}$

Explanation:

Step1: Apply exponent product rule

When multiplying terms with the same base, add exponents: $x^m x^n = x^{m+n}$. So, $x^{\frac{2}{3}}x^{\frac{1}{2}} = x^{\frac{2}{3}+\frac{1}{2}}$.

Step2: Add the fractions

Find a common denominator (6) to add $\frac{2}{3}$ and $\frac{1}{2}$:
$\frac{2}{3}+\frac{1}{2} = \frac{4}{6}+\frac{3}{6} = \frac{7}{6}$

Answer:

$\frac{7}{6}$