Question

use the quotient rule to simplify.\\(\frac{-8a^{4}b^{6}c^{13}}{2a^{2}b^{3}c^{11}}\\)\\(\frac{-8a^{4}b^{6}c^{13}}{2a^{2}b^{3}c^{11}} = \square\\)\\((type your answer using exponential notation.)\\)

Explanation:

Step1: Separate coefficients & variables

$\frac{-8}{2} \cdot \frac{a^4}{a^2} \cdot \frac{b^6}{b^3} \cdot \frac{c^{13}}{c^{11}}$

Step2: Simplify coefficient

$\frac{-8}{2} = -4$

Step3: Apply quotient rule to $a$

$\frac{a^4}{a^2} = a^{4-2} = a^2$

Step4: Apply quotient rule to $b$

$\frac{b^6}{b^3} = b^{6-3} = b^3$

Step5: Apply quotient rule to $c$

$\frac{c^{13}}{c^{11}} = c^{13-11} = c^2$

Step6: Multiply all simplified terms

$-4 \cdot a^2 \cdot b^3 \cdot c^2$

Answer:

$-4a^2b^3c^2$