Question

Medal given! Please help with 3.a, b,c and 4 a,b,c,d

Answer 1

\[256^x=\frac{1}{16}\]?

Answer 2

I'm guessing we would have to do the inverse?

Answer 3

\(256=16^2\)

Answer 4

so
\[256^x=(16^2)^x=16^{2x}\]

Answer 5

your equation is now
\[16^{2x}=\frac{1}{16}\] or
\[16^{2x}=16^{-1}\] making
\[2x=-1\]

Answer 6

and then solving for x we would divide both sides by 2 so x=-1/2?

Answer 7

yes

Answer 8

ok :)) so for a i'd need to raise both x and 3 to the 3rd power?

Answer 9

\[(x-3)^3=64\]take the cubed root of both sides

Answer 10

on no no, \((x-3)^2\neq x^2-3^3\) you don't want to do that at all
do you know what the cubed root of \(64\) is?

Answer 11

no is a fine answer, i am just asking if you know it
if not, i will tell you

Answer 12

i'm not sure off the top of my head..

Answer 13

ok it is 4, and the reason we would know it is because \(4^3=4\times 4\times 4=16\times 4=64\)

Answer 14

so if \((x-3)^3=64\) then you know \(x-3=4\)

Answer 15

so to find x you would basically at 3 on both sides of the equal sign to find x?

Answer 16

add*

Answer 17

x=7

Answer 18

yes

Answer 19

oh ok :-) thank you

Answer 20

yw

Answer 21

and for c it's just simply raising the 1/5 reciprocal?

Answer 22

for c it is
\[x=\sqrt[5]{32}^4\]

Answer 23

do you know that the fifth root of 32 is?

Answer 24

not quite sure

Answer 25

actually yes i do! :) it's 2^5=32

Answer 26

tada!

Answer 27

so \(\sqrt[5]{32}=2\)
your last job it to find \(2^4\)

Answer 28

which is 8

Answer 29

nope

Answer 30

\(2^3=8\)

Answer 31

16

Answer 32

yup

Answer 33

yay!

Answer 34

yay indeed!

Answer 35

Thank you so much.. you really helped me a lot :)

Answer 36

If you don't mind I wanted to ask you really quick if there is a specific method to do 4 a-d

Answer 37

@satellite73

Answer 38

sure

Answer 39

for a, count from the places you have to move to the left to get from \(37,000,000\) to the decimal in \(3.7\)

Answer 40

i count seven places, making
\[37,000,000=3.7\times 10^7\]

Answer 41

oh ok :) thanks so much!!

Answer 42

are the rest ok?

Answer 43

in b you have to count to the left 4 places, making
\[0.000801=8.01\times 10^{-4}\]

Answer 44

sorry, i meant count to the right

Answer 45

yw