Certainly! Let's go through the calculation step by step, given the values [tex]\( a = 3 \)[/tex], [tex]\( b = -4 \)[/tex], and [tex]\( c = 8 \)[/tex].
We need to evaluate the expression:
[tex]\[ \frac{a \cdot b^2}{c + 12} \][/tex]
1. Square the value of [tex]\( b \)[/tex]:
Given [tex]\( b = -4 \)[/tex]:
[tex]\[
b^2 = (-4)^2 = 16
\][/tex]
2. Multiply [tex]\( a \)[/tex] by [tex]\( b^2 \)[/tex]:
Given [tex]\( a = 3 \)[/tex] and from step 1, [tex]\( b^2 = 16 \)[/tex]:
[tex]\[
a \cdot b^2 = 3 \cdot 16 = 48
\][/tex]
3. Add 12 to [tex]\( c \)[/tex]:
Given [tex]\( c = 8 \)[/tex]:
[tex]\[
c + 12 = 8 + 12 = 20
\][/tex]
4. Divide the product from step 2 by the sum from step 3:
From step 2, we have [tex]\( a \cdot b^2 = 48 \)[/tex] and from step 3, [tex]\( c + 12 = 20 \)[/tex]:
[tex]\[
\frac{a \cdot b^2}{c + 12} = \frac{48}{20} = 2.4
\][/tex]
So, the evaluated expression is:
[tex]\[ \boxed{2.4} \][/tex]
