Evaluate [tex]$2 x^4 y$[/tex] for [tex]$x=2$[/tex] and [tex][tex]$y=4$[/tex][/tex].

A. [tex]$\frac{1}{2}$[/tex]

B. [tex]$-64$[/tex]

C. [tex]$\frac{1}{8}$[/tex]



Answer :

To evaluate the expression [tex]\( 2x^4y \)[/tex] given [tex]\( x = 2 \)[/tex] and [tex]\( y = 4 \)[/tex], follow these steps:

1. Substitute the given values into the expression:
Substitute [tex]\( x = 2 \)[/tex] and [tex]\( y = 4 \)[/tex] into the expression [tex]\( 2x^4y \)[/tex].

So, the expression becomes:
[tex]\[ 2(2)^4(4) \][/tex]

2. Evaluate the exponent:
Calculate [tex]\( 2^4 \)[/tex]:
[tex]\[ 2^4 = 2 \times 2 \times 2 \times 2 = 16 \][/tex]

3. Substitute the result of the exponent into the expression:
Now the expression is:
[tex]\[ 2 \cdot 16 \cdot 4 \][/tex]

4. Perform the multiplications:
First, multiply [tex]\( 2 \)[/tex] by [tex]\( 16 \)[/tex]:
[tex]\[ 2 \times 16 = 32 \][/tex]

Then multiply the result by [tex]\( 4 \)[/tex]:
[tex]\[ 32 \times 4 = 128 \][/tex]

So, the value of the expression [tex]\( 2x^4y \)[/tex] for [tex]\( x = 2 \)[/tex] and [tex]\( y = 4 \)[/tex] is [tex]\( 128 \)[/tex].

Comparing this result to the provided options:
- [tex]\( \frac{1}{2} \)[/tex]
- [tex]\( -64 \)[/tex]
- [tex]\( \frac{1}{8} \)[/tex]

None of the provided options match the correct result of [tex]\( 128 \)[/tex]. Therefore, it seems there might have been an error in the provided options. The true result is [tex]\( 128 \)[/tex].