Question

evaluate the left hand side to find the value of $a$ in the equation in simplest form.
$\frac{x^{\frac{5}{3}}}{x^{\frac{6}{5}}}=x^{a}$

Explanation:

Step1: Apply exponent division rule

When dividing like bases, subtract exponents: $\frac{x^m}{x^n}=x^{m-n}$. So,
$$x^{\frac{5}{3}-\frac{6}{5}} = x^a$$

Step2: Compute exponent difference

Find common denominator (15) to subtract fractions:
$$\frac{5}{3}-\frac{6}{5} = \frac{25}{15}-\frac{18}{15} = \frac{7}{15}$$

Step3: Equate exponents

Since bases are equal, exponents must be equal:
$$a = \frac{7}{15}$$

Answer:

$\frac{7}{15}$