Question

What is the value of the expression? 1/4^3

Answer 1

1/64

Answer 2

@jpenrod okay, now explain how you got that

Answer 3

Yes please explain 'cause I just don't understand.

Answer 4

4x4=16 16x4= 64 1/64 simple

Answer 5

So you just do 4x4x4=64 as the bottom part then just bring the 1 over to the top?

Answer 6

you understand that 4^3 = 4*4*4, right?

Answer 7

yes, i think i understand now. i should of just worked it out.

Answer 8

What is the value of the expression?
2/4^-3
How do I do this one with the negative power?

Answer 9

so 1/(4^3) = 1/(4*4*4) = 1/64

also, by the properties of exponents, (1/4)^3 also equals 1/64: (1/4)*(1/4)*(1/4)

and finally, you might see this written as 4^-3, which is equivalent, because a^-n = 1/a^n

Answer 10

good to be familiar with all the different ways you might see the same thing, because, well, you'll be seeing all of them sooner or later :-)

Answer 11

do you have a few more of those? you can do them and I'll check your work

Answer 12

A. 1/32


B. 1/6


C. 128

D. 256
OK So the answer is A.?

Answer 13

what's the problem? :-)

Answer 14

The one we just did, the second one.

Answer 15

oh, I didn't see that you snuck that in there, sorry! :-)

Answer 16

no its 128

Answer 17

2/4^-3

well, let's first convert it to a positive power: if it's a negative power, we make it positive, and put it on the other side of the division line, so it becomes
2*4^3

Answer 18

2/64 = 2*4^3
Is that right?

Answer 19

2/64 = 2/4^3 or 2 * 4^-3

but are we talking about a different problem now? the second one you showed was

2/4^-3 or

2
------
4^-3

and because 4^-3 = 1/4^3

we can write it as

2
------
(1/4^3)

dividing a fraction by a fraction, you invert the fraction in the denominator and multiply:

2 * (4^3/1) = 2*4^3 = 2*64 = 128, like jpenrod said

Answer 20

Sorry, OK The problem is

What is the value of the expression? 2/4^-3

A. 1/32


B. 1/6


C. 128

D. 256

Answer 21

right, so the answer is C. 128

do you understand how we got that answer?

Answer 22

Yeah...I think so. :D

Answer 23

well, let's try another and find out :-)

what is the value of 4/3^-2?

Answer 24

What about this one..

What value of k solves the equation?

K-4 = 1/256


A. –64

B. 8

C. 4

D. 64

Answer 25

let's do mine first :-)

Answer 26

4/-18? I don't really think that's it. I'm bad with negatives

Answer 27

remember: if you have a negative exponent, make it a positive exponent and put the quantity on the other side of the division bar.

4 4*3^2
------ = ------- = ?
3^-2 1

Answer 28

OK so 4/9? I know it somehow gets to 36, right?

Answer 29

no, we had

4*3^2
-----
1

3^2 = 9, right

4*9
----
1

= 36

Answer 30

okay, your problem, is that actually supposed to be k^-4 ?

Answer 31

because the answer to k-4 = 1/256 doesn't appear among the answer choices

Answer 32

woops, sorry. k^-4

Answer 33

right. so what is another way of writing k^-4?

Answer 34

sorry, computer issues....IDK, is there

Answer 35

@Yuba @whpalmer4

Answer 36

k^-4 = 1/k^4, right? negative exponent becomes a positive exponent on the other side of the division bar

Answer 37

so that gives us

1 1
--- = -----
k^4 256

how could you solve that?

Answer 38

Find the common denominator?

Answer 39

you could "flip" both sides

Answer 40

or cross multiply

Answer 41

what is K^4

Answer 42

if those fractions are equal, and the numerators are identical, don't the denominators have to be equal?

Answer 43

If I have

1 1
-- = --
x 4

doesn't x have to equal 4?

Answer 44

that's the same as "flipping" both sides. cross-multiplying would give you the same thing:

4*1 = x*1
4 = x

so here we have k^4 = 256
what is the value for k such that k*k*k*k = 256?

Answer 45

4^4 = 256......right?

Answer 46

So is the answer 4

Answer 47

if k = 4, then

(4)^-4 = 1/256
1/(4^4) = 1/256
1/(256) = 1/256
which is true.
yes, the answer is 4.

Answer 48

YAY!

Answer 49

good job!