Evaluate 1/2a^–4b^2 for a = –2 and b = 4.

A.)2
B.)1/2
C.)3
D.)4

I think it is D.
Thabk You.

assuming the 1/2 is a coefficient, we have

(1/2) (-2)^-4 (4)^2
(1/2) (1/(-2)^4) (4)^2
(1/2) (1/16) (16)
1/2

(B)

Thank You.

B is right!!

Well, well, well! Let's put on our math hats and solve this equation!

We have 1/2a^–4b^2, with a = -2 and b = 4. Now, remember that negative signs can be a bit moody sometimes, so we need to keep an eye on them.

Plugging in the values, we get:

1/2(-2)^(-4)(4)^2

Now, time to calculate. Let's start with those negative signs. A negative sign raised to an even power becomes positive, while a negative sign raised to an odd power remains negative. In this case, we have (-2)^(-4), which gives us 1/(-2)^4.

Using our handy-dandy calculator, we find that -2 raised to the power of 4 is 16. So, we have 1/16.

Now, let's move on to the next part of our equation. We have 1/16 * (4)^2.

Again, using our trusty calculator, 4 squared is 16. So, we have 1/16 * 16.

And guess what? 1/16 * 16 equals 1!

So, after all that math magic, we find that 1/2a^–4b^2, with a = -2 and b = 4, is equal to... drumroll, please... 1!

So, my friend, the correct answer is... *drumroll gets louder*... B.) 1/2!

Keep up the great work, and feel free to ask if you need any more math humor or assistance!

To evaluate the expression 1/2a^(-4)b^2 for a = -2 and b = 4, we substitute the given values into the expression and simplify.

First, substitute the given values:
1/2(-2)^(-4)(4)^2

Next, evaluate the exponent of -2^(-4):
1/2(1/(-2)^4)(4)^2

Simplify the expression inside the parentheses:
1/2(1/16)(4)^2

Evaluate 4^2:
1/2(1/16)(16)

Simplify 1/16 and 16:
1/2(1/16)(1)

Evaluate 1/16 * 1:
1/32

Therefore, when a = -2 and b = 4, 1/2a^(-4)b^2 is equal to 1/32.

The correct answer is not D, but rather B.) 1/32.

Please note that it's important to be careful with negative exponents. When a negative exponent appears, it indicates that the base should be inverted. Additionally, remember to follow the order of operations (PEMDAS/BODMAS) when simplifying expressions.