Evaluate the left hand side to find the value of $$ a $$ in the equation simplest form. $$ \frac{x^{2}}{x^{\frac{5}{6}}}=x^{a} $$

Question

UpStudy AI · Accepted Answer

To find the value of $$ a $$ in the equation

$$
\frac{x^{2}}{x^{\frac{5}{6}}} = x^{a},
$$

we can simplify the left-hand side (LHS) using the properties of exponents.

### Step 1: Simplify the LHS

Recall the exponent rule:

$$
\frac{x^{m}}{x^{n}} = x^{m - n}.
$$

Applying this rule to the LHS:

$$
\frac{x^{2}}{x^{\frac{5}{6}}} = x^{2 - \frac{5}{6}}.
$$

### Step 2: Subtract the Exponents

To subtract the exponents, we need to have a common denominator:

$$
2 = \frac{12}{6}.
$$

So,

$$
2 - \frac{5}{6} = \frac{12}{6} - \frac{5}{6} = \frac{7}{6}.
$$

### Step 3: Equate the Exponents

Now, the equation becomes:

$$
x^{\frac{7}{6}} = x^{a}.
$$

Since the bases are the same, the exponents must be equal:

$$
a = \frac{7}{6}.
$$

### Final Answer

$$
a = \frac{7}{6}.
$$
$$ a = \frac{7}{6} $$

Evaluate the left hand side to find the value of \( a \) in the equation simplest form. \[ \frac{x^{2}}{x^{\frac{5}{6}}}=x^{a} \]