Questions: Use the properties of exponents to simplify the following as much as possible. Assume all bases are positive. [ x^frac56 / x^frac12 = ]

$Use the properties of exponents to simplify the following as much as possible. Assume all bases are positive. [ x^frac56 / x^frac12 = ]$

Transcript text: Use the properties of exponents to simplify the following as much as possible. Assume all bases are positive. \[ \frac{x^{\frac{5}{6}}}{x^{\frac{1}{2}}}= \] $\square$ Question Help: $\square$ Message instructor Submit Question

Solution

Solution Steps

To simplify the given expression using the properties of exponents, we can use the quotient rule for exponents, which states that $\frac{a^m}{a^n} = a^{m-n}$. Here, we will subtract the exponent in the denominator from the exponent in the numerator.

Step 1: Identify the Exponents

We start with the given expression: \[ \frac{x^{\frac{5}{6}}}{x^{\frac{1}{2}}} \]

Step 2: Apply the Quotient Rule for Exponents

Using the quotient rule for exponents, $\frac{a^m}{a^n} = a^{m-n}$, we subtract the exponent in the denominator from the exponent in the numerator: \[ \frac{5}{6} - \frac{1}{2} \]

Step 3: Simplify the Exponents

Convert the fractions to a common denominator and perform the subtraction: \[ \frac{5}{6} - \frac{1}{2} = \frac{5}{6} - \frac{3}{6} = \frac{2}{6} = \frac{1}{3} \]