Question $\frac{7 x^{3}}{14 x}$

Studdy Solution

STEP 1

1. We are asked to simplify the given expression.
2. The expression involves a fraction with a polynomial in the numerator and a monomial in the denominator.
3. The variable $x$ is non-zero to avoid division by zero.

STEP 2

1. Simplify the coefficients in the fraction.
2. Simplify the powers of $x$ in the fraction.

STEP 3

Identify and simplify the coefficients in the fraction $\frac{7 x^{3}}{14 x}$ .
$\frac{7}{14} = \frac{1}{2}$
Thus, the expression becomes:
$\frac{1}{2} \times \frac{x^{3}}{x}$

STEP 4

Simplify the powers of $x$ in the fraction $\frac{x^{3}}{x}$ .
Using the property of exponents $\frac{x^a}{x^b} = x^{a-b}$ , we have:
$x^{3-1} = x^{2}$
Thus, the expression becomes:
$\frac{1}{2} \times x^{2} = \frac{x^{2}}{2}$
The simplified expression is:
$\frac{x^{2}}{2}$

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