To simplify the expression [tex]\(\frac{8 c^3 d^2}{4 c d^2}\)[/tex], we will follow a systematic step-by-step approach.
Step 1: Simplify the coefficients.
The coefficients in the numerator and the denominator are 8 and 4, respectively. Divide 8 by 4:
[tex]\[
\frac{8}{4} = 2
\][/tex]
Step 2: Simplify the [tex]\(c\)[/tex] terms.
In the numerator, we have [tex]\(c^3\)[/tex], and in the denominator, we have [tex]\(c\)[/tex]. Apply the laws of exponents to divide these terms:
[tex]\[
\frac{c^3}{c} = c^{3-1} = c^2
\][/tex]
Step 3: Simplify the [tex]\(d\)[/tex] terms.
In the numerator, we have [tex]\(d^2\)[/tex], and in the denominator, we also have [tex]\(d^2\)[/tex].
[tex]\[
\frac{d^2}{d^2} = 1
\][/tex]
Since any term divided by itself equals 1, the [tex]\(d\)[/tex] terms cancel out.
Step 4: Combine the simplified results.
After simplifying the coefficients and the variables, we combine our results:
[tex]\[
2 \cdot c^2 \cdot 1 = 2c^2
\][/tex]
Therefore, the simplified expression is:
[tex]\[
\frac{8 c^3 d^2}{4 c d^2} = 2c^2
\][/tex]
This is the final simplified form of the given expression.
