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].
