Of course! Let's evaluate the given expression step by step using the values provided: [tex]\( x = 6 \)[/tex], [tex]\( y = -4 \)[/tex], and [tex]\( z = 14 \)[/tex].
The expression to evaluate is:
[tex]\[
\frac{2x \cdot 2y^3}{5z^2}
\][/tex]
### Step 1: Calculate [tex]\( 2x \)[/tex]
First, we calculate [tex]\( 2x \)[/tex]:
[tex]\[
2x = 2 \cdot 6 = 12
\][/tex]
### Step 2: Calculate [tex]\( 2y^3 \)[/tex]
Next, we need to calculate [tex]\( 2y^3 \)[/tex]. We start by calculating [tex]\( y^3 \)[/tex]:
[tex]\[
y^3 = (-4)^3 = -64
\][/tex]
And then calculate [tex]\( 2y^3 \)[/tex]:
[tex]\[
2y^3 = 2 \cdot (-64) = -128
\][/tex]
### Step 3: Calculate [tex]\( 5z^2 \)[/tex]
Now we calculate [tex]\( 5z^2 \)[/tex]. We start by calculating [tex]\( z^2 \)[/tex]:
[tex]\[
z^2 = 14^2 = 196
\][/tex]
And then calculate [tex]\( 5z^2 \)[/tex]:
[tex]\[
5z^2 = 5 \cdot 196 = 980
\][/tex]
### Step 4: Combine the results
Finally, we combine all the computed parts to evaluate the expression:
[tex]\[
\frac{2x \cdot 2y^3}{5z^2} = \frac{12 \cdot (-128)}{980}
\][/tex]
### Step 5: Simplify the fraction
[tex]\[
12 \cdot (-128) = -1536
\][/tex]
Thus, the expression becomes:
[tex]\[
\frac{-1536}{980} \approx -1.5673469387755101
\][/tex]
So the evaluated result of the expression [tex]\(\frac{2 x \cdot 2 y^3}{5 z^2}\)[/tex] is [tex]\(-1.5673469387755101\)[/tex].
