Question

Evaluate

Answer 1

\[\frac{ 1 }{ 2 }a ^{-4}b ^{2} \]
b=-2 and b= 4

Answer 2

you have b=-2 and b=4. Do you mean a= -2 ?

Answer 3

Oh yes sorry xD

Answer 4

can you erase the "a" and put in (-2) in its place
and erase b and put 4 in its place ?
what do you get ?

Answer 5

remember that the (-2) goes with a (the whole thing is raised to the -4 power

Answer 6

Wait sorry I messed up\[\frac{ 1 }{ 2 }-2^{-4}4^{2}\]

Answer 7

Idk if I'm doing this correctly.

Answer 8

close, but you should put in the parens around the -2
\[ \frac{1}{2} (-2)^{-4} 4^2 \]

Answer 9

Now, this is a tricky exercise, because we could evaluate it directly if we had a calculator, but I suppose your teacher doesn't want that, so to do it we'll have to simplify the expression in a more simple form:
\[\frac{ 1 }{ 2 }a ^{-4}b ^{2}\]
\[\frac{ 1 }{ 2a ^{4} }b ^{2}\]
\[\frac{ b ^{2} }{ 2a ^{4} }\]
and for a=-2 and b=4
\[\frac{ 4^{2} }{ 2(-2^{4}) }=\frac{ 16 }{ -32 }=-\frac{ 1 }{ 2 }\]

Answer 10

There is no -1/2 in the answer options @Owlcoffee

Answer 11

There's only:
2
1/2
3
4

Answer 12

4^2 means 4*4

the exponent -4 means " flip " and change the -4 to +4
in other words
\[ (-2)^{-4} = \frac{1}{(-2)^4} \]

Answer 13

you could try to figure it out..

Answer 14

what is 4*4 ?

Answer 15

and what is -2* -2 * -2 * -2 ?

Answer 16

so the answer is 1/2

Answer 17

4 x 4 = 16
-2 x -2 x -2 x -2 = 16

Answer 18

yes, so now you have
\[ \frac{1}{2}\frac{16}{16} \]

Answer 19

and 16 divided by itself is 1

Answer 20

And then it'll equal to what @Owlcoffee said.

Answer 21

Cuz you multiply.

Answer 22

1 x 1/2

Answer 23

Here are the steps
\[ \frac{1}{2} (-2)^{-4} 4^2 \\ \frac{1}{2} \frac{4\cdot 4}{(-2)^4} \\
\frac{1}{2} \frac{4\cdot 4}{(-2 \cdot -2 \cdot -2 \cdot -2)} \\
\frac{1}{2} \frac{16}{16} \\
\frac{1}{2}
\]

Answer 24

the tricky part is knowing that the -2 goes "inside" the exponent. in other words
(-2)^4 is different from - 2^4 (that first is positive, the second is negative)
also, remember that a negative exponent means "flip"

Answer 25

Oh now I understand what you did.

Answer 26

I assume you know that they "invented" 2^5 as short cut to write 2*2*2*2*2
(very helpful for numbers like 10^23. ) Exponents are just a short cut to writing out ill those multiplies.

Answer 27

Oh yes, I know cx I just didn't understand how you got the exponent from negative to positive but now I understand cx

Answer 28

Do you mind helping me with one more?

Answer 29

@phi

Answer 30

Please make a new post.