Question

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

A.
12

B.
64

C. 1/64


D.
1/12

Answer 1

@Compassionate @tHe_FiZiCx99

Answer 2

It's 64

Answer 3

\[x ^{-y}=(1/x)^{y}\]

Answer 4

will u help me with 2 more

Answer 5

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

Answer 6

128

Answer 7

What value of k solves the equation?

k^-3 = 1/27

Answer 8

\[k^{-3} = \frac{1}{27}\]\[k^{-3} = \frac{1}{k^3}\]\[\frac{1}{k^3} = \frac{1}{27}\]any ideas about what \(k\) is?

Answer 9

ummm -81

Answer 10

-9

Answer 11

well, for \[\frac{1}{k^3} = \frac{1}{27}\]we need to have \[k^3 = k*k*k= 27\]right?

Answer 12

yea

Answer 13

can you think of a number that makes that true?
1*1*1 = 1
2*2*2 = 8

Answer 14

its 3

Answer 15

bingo!

Answer 16

or -3???

Answer 17

good question, but no, not if there is an even power involved.

\[x^2=9\] for both \(x=3\) and \(x=-3\)
however, we have
\[x^3=27\]
\[3*3*3 = 27\]
\[(-3)*(-3)*(-3) = -27\]

Answer 18

sorry, "not if there is an ODD power involved"

Answer 19

What value of n solves the equation 4^n + 1/64?

Answer 20

that's not an equation, as there is no equals sign :-)

Answer 21

wait

Answer 22

What value of n solves the equation 4^n = 1/64

Answer 23

\[4^n = \frac{1}{64}\]

Any ideas on whether \(n\) is positive or negative?

Answer 24

positive

Answer 25

well, sadly, no :-)

if it positive, then we are going to have something like

\[4*4*4 = \frac{1}{64}\] (for some number of 4's)

But that's not ever going to be true, is it?

Answer 26

No, we need a negative exponent, because we need it to look something like
\[\frac{1}{4}*\frac{1}{4}*... = \frac{1}{64}\]right?

Answer 27

yea?

Answer 28

A negative exponent would let us do this:
\[4^n = \frac{1}{4^m} = \frac{1}{64}\](if \(m = -n\))

Answer 29

So that makes our problem be
\[4^m = 64\]How many times do you have to multiply 4 with itself to get 64?

4=4
4*4=16
4*4*4=64
4*4*4*4=256
etc.

Answer 30

okay thanks will u help me with some more???

Answer 31

So what is the answer for that problem?
\[4^n = \frac{1}{64}\]\[n=\]