Question

help!

Answer 1

@TheSmartOne @rebeccaxhawaii

Answer 2

@Jakesaurus1127

Answer 3

@jim_thompson5910

Answer 4

What do you have so far?

Answer 5

nothing..

Answer 6

@jim_thompson5910 ???

Answer 7

Have you heard of the rule that
\[\LARGE \left(x^y\right)^z = x^{y*z}\]
?

Answer 8

yes

Answer 9

So we'll use this rule to break down the expression

Answer 10

ok!

Answer 11

For instance
\[\LARGE \left(3^{8}*2^{-5}*9^{0}\right)^{-2} = 3^{8*(-2)}*2^{-5*(-2)}*9^{0*(-2)}\]
Notice how the outer exponent (-2) is multiplied by EVERY exponent inside. It's kinda like distributing.

Answer 12

make sense?

Answer 13

yea

Answer 14

what is 8*(-2) equal to?

Answer 15

-16

Answer 16

how about -2*(-5) ?

Answer 17

10

Answer 18

So this means
\[\Large \left(3^{8}*2^{-5}*9^{0}\right)^{-2} = 3^{8*(-2)}*2^{-5*(-2)}*9^{0*(-2)}\]
\[\Large \left(3^{8}*2^{-5}*9^{0}\right)^{-2} = 3^{-16}*2^{10}*9^{0}\]
\[\Large \left(3^{8}*2^{-5}*9^{0}\right)^{-2} = 3^{-16}*2^{10}*1\]
\[\Large \left(3^{8}*2^{-5}*9^{0}\right)^{-2} = 3^{-16}*2^{10}\]

Answer 19

Do you agree?

Answer 20

yes!

Answer 21

ok now onto the piece
\[\Large \left(\frac{2^{-2}}{3^{3}}\right)^{4}\]

Answer 22

The \(\Large 3^3\) in the denominator can be written as \(\Large 3^{-3}\)


In other words,

\[\Large \frac{1}{3^3} = 3^{-3}\]

do you agree?

Answer 23

@volleyballlover55 the answer to your other problem was \[(3^{8}*2^{-5}*9^{0})^{-2}*(\frac{2^{-2}}{3^{3}})^{4}*3^{28}\]\[(6^{3})^{-2}*(\frac{.25}{27})^{4}*22,876,792,454,961\]\[0.0000214335*0.0092592592*22,876,792,454,961\]\[4540090.07357\] sorry it took so long.

Answer 24

isnt the answer 4?

Answer 25

@jim_thompson5910 is he correct?

Answer 26

do you agree with what I posted last @volleyballlover55 ?

Answer 27

yes..

Answer 28

So,
\[\Large \left(\frac{2^{-2}}{3^{3}}\right)^{4}=\left(2^{-2}*3^{-3}\right)^{4}\]

Answer 29

What do you get when you multiply the outer exponent (4) by the inner exponents?

Answer 30

um, idk..

Answer 31

first tell me what the inner exponents are

Answer 32

any ideas @volleyballlover55 ?

Answer 33

um.. 531441/256

Answer 34

I'd leave it in exponent form

Answer 35

example: instead of saying 1024, write 2^10

Answer 36

do you know what I mean by "exponent form" ?

Answer 37

yes..

Answer 38

Use the rule
\[\Large \left(x^y\right)^z = x^{y*z}\]
and tell me what
\[\Large \left(2^{-2}\right)^{4}\]
is equal to in exponent form

Answer 39

1/256

Answer 40

the exponents are -2 and 4. Multiply them to get -8

so
\[\Large \left(2^{-2}\right)^{4}=2^{-2*4}=2^{-8}\]
That's what I meant by "exponent form"

Answer 41

Let's try another for practice. What is (3^5)^7 in exponent form?

Answer 42

can we please just get onto the problem.. i need to finish it..

Answer 43

If you aren't going to work with me, then I can't help you. Sorry