Absolutely, let's solve the expression step-by-step for the given values of [tex]\( a \)[/tex], [tex]\( b \)[/tex], and [tex]\( c \)[/tex].
We have:
[tex]\[
\frac{3}{16} a b c^2
\][/tex]
Given:
[tex]\[
a = 4
\][/tex]
[tex]\[
b = 8
\][/tex]
[tex]\[
c = 3
\][/tex]
First, substitute the given values into the expression:
[tex]\[
\frac{3}{16} \cdot 4 \cdot 8 \cdot 3^2
\][/tex]
Next, compute [tex]\( 3^2 \)[/tex]:
[tex]\[
3^2 = 9
\][/tex]
Now, substitute [tex]\( 9 \)[/tex] back into the expression:
[tex]\[
\frac{3}{16} \cdot 4 \cdot 8 \cdot 9
\][/tex]
Next, multiply the coefficients and constants together:
[tex]\[
4 \cdot 8 = 32
\][/tex]
[tex]\[
32 \cdot 9 = 288
\][/tex]
Now we have:
[tex]\[
\frac{3}{16} \cdot 288
\][/tex]
Finally, divide [tex]\( 288 \)[/tex] by [tex]\( 16 \)[/tex] and then multiply by [tex]\( 3 \)[/tex]:
[tex]\[
\frac{288}{16} = 18
\][/tex]
[tex]\[
3 \cdot 18 = 54
\][/tex]
Thus, the result of the expression is:
[tex]\[
54
\][/tex]
