Question

simplify. express your answer using positive exponents.
\\(\frac{4mn^3}{2m^8n \cdot mn}\\)

Explanation:

Step1: Simplify denominator terms

First, multiply the terms in the denominator by adding exponents of like bases.
$2m^8n \cdot mn = 2m^{8+1}n^{1+1} = 2m^9n^2$

Step2: Rewrite the original expression

Substitute the simplified denominator back into the fraction.
$\frac{4mn^3}{2m^9n^2}$

Step3: Simplify coefficients and variables

Divide coefficients, and subtract exponents of like bases (subtract denominator exponents from numerator exponents).
$\frac{4}{2} \cdot m^{1-9} \cdot n^{3-2} = 2m^{-8}n^{1}$

Step4: Convert to positive exponents

Rewrite negative exponents as positive exponents in the denominator.
$2 \cdot \frac{n}{m^8} = \frac{2n}{m^8}$

Answer:

$\frac{2n}{m^8}$