Question

use the quotient rule to simplify the given expression.\\(\frac{3d^{8}c^{3}}{33d^{8}c}\\)\\(\frac{3d^{8}c^{3}}{33d^{8}c} = square\\)(type your answer using exponential notation. use positive exponents on

Explanation:

Step1: Simplify the coefficient

Simplify the fraction of the coefficients 3 and 33. $\frac{3}{33} = \frac{1}{11}$

Step2: Apply quotient rule to \(d\) terms

For the \(d\) terms, use the quotient rule $ \frac{a^m}{a^n}=a^{m - n} $. Here, \(m = 8\), \(n = 8\), so $ \frac{d^{8}}{d^{8}}=d^{8 - 8}=d^{0} = 1$ (since any non - zero number to the power of 0 is 1)

Step3: Apply quotient rule to \(c\) terms

For the \(c\) terms, use the quotient rule. Here, \(m = 3\), \(n = 1\), so $ \frac{c^{3}}{c^{1}}=c^{3 - 1}=c^{2}$

Step4: Combine the results

Multiply the results from step 1, step 2 and step 3. We have $\frac{1}{11}\times1\times c^{2}=\frac{c^{2}}{11}$

Answer:

$\frac{c^{2}}{11}$