Question

2(x+4)^4/3 = 512

Answer 1

first divide both sides by 2.

Answer 2

i get (x+4)^4/3 = 256

Answer 3

right.

now..take the 4th root of both sides

Answer 4

x^4 + 256 = 256 ?

Answer 5

oh wait

Answer 6

sorry, can you explain why you take the 4th root?

Answer 7

because you have (x+4)^4/3

this can also be written as \[\Large \implies [(x+4)^{\frac 13} ]^4\]
to get rid of that raised to 4, you have to take the 4th root

does that make sense?

Answer 8

yes so it would be \[\sqrt[4]{x} + \sqrt[4]{4} = 4\]

Answer 9

no...

\[\sqrt{(a+b)^2} \implies a+b\]
\[\sqrt{(a+b)^2} \ne \sqrt a + \sqrt b\]
do you get what im implying?

Answer 10

so would the x and the 4 that are under the sqrt signs be to the 3rd power as well?

Answer 11

no..

Answer 12

let me make another metaphor...
\[\huge \sqrt{(a+b)^{\frac 23}} \implies (a+b)^{\frac 13} \]

Answer 13

now do you get it?

Answer 14

i'm sorry, i still don't get it

Answer 15

my point is...if you take the 4th root of (x+4)^4/3 only 4 gets canceled. everything else should look the same

Answer 16

Since you get get (x+4)^4/3 = 256

We need to do the inverse of the powers on the left side.
Exponents multiply and divide.
Cube both sides of the equation to get rid of the 1/3 power:
(x + 4)^4 = 256^3

Take the 4th root of both side to get rid of the ^4:
x + 4 = 256^3/4

x+ 4 = 64
x = 60

Answer 17

\[\huge \sqrt[4]{(x+4)^{\frac 43}} \implies \sqrt[\cancel 4]{(x+4)^{\frac {\cancel 4}3}} \implies (x+4)^{\frac 13}\]

dow do you get what i mean?

Answer 18

but how come it doesn't seem like the 4th root is taken for the 256 on the right side?

Answer 19

oh it is... im just showing the left side because you were wrong there. your right side was right

Answer 20

\[\huge (x+4)^{\frac 13} = 4\]
still following?

Answer 21

yes

Answer 22

good. now cube both sides to get rid of that raised to 1/3

Answer 23

so it would be x^3 + 64 = 64

Answer 24

no. again...you don't touch the ones INSIDE the parenthesis

Answer 25

you just cancel the exponents

Answer 26

oh yes, so it would be x+4 = 64, then subtract 4 from both sides and get x = 60

Answer 27

right

Answer 28

got it, thank you very much! :)

Answer 29

welcome

Answer 30

Corollary: raise each side to the reciprocal of 4/3. This gets rid of the 4/3 power, skips unnecessary steps, and you arrive at x + 4 = 64... x = 60 quickly

Answer 31

is this after you divide the 2 on both sideS?

Answer 32

you can also do much more advanced steps to get the answer in a second...i wonder why we don't do that

Answer 33

it is, got the same answer doing it your way. thank you very much :)

Answer 34

Yes that is after you divide by 2.