Question

Explain the process where: X = 16^(3/2)
X = (root 16)^3

Answer 1

First we have to split power of 16 can you try ?

Answer 2

oh, no I already know how to do it... its just I don't understand why the denominator becomes 2 root and why the numerator becomes the power

Answer 3

okay let me explain it

Answer 4

ok

Answer 5

We were having x^(2/3) = 16
We have to solve it for x so need to reduce power of x to one

Answer 6

Getting this ???

Answer 7

yeah

Answer 8

okay
So here we have to use reciprocal of power like if fraction is like a/b then its reciprocal is b/a so what would be reciprocal of power of x which is ( 2 / 3 ) ?

Answer 9

\[\frac{ 3 }{ 2 }\]

Answer 10

correct so we need to take ( 3/2 ) power on both sides
So we get x^( 2/3) * ( 3/2) = 16^(3/2)
So it becomes x = 16^( 3 / 2 ) getting this ???

Answer 11

Yeah

Answer 12

Now we need to split power of 16 using rule of multiplication of power
Are you familiar with rule a^( m)*( n ) = a^ m * n ?

Answer 13

See the attachment.

Answer 14

oh,ok

Answer 15

Are you getting this ?
So we can rewrite it as 16^ ( 3 ) * ( 1/2 ) correct ?

Answer 16

Yeah

Answer 17

16^(1/2)*(3)
So first we would find out 16^( 1/2) = ---- ? what is square root of 16 ?

Answer 18

4

Answer 19

Perfect
So we get 16^((1/2) * 3) = 4^3 = ----- ?
So 4 cube = ----- ???

Answer 20

We are about to finish it last step 4^3 = ---- ?

Answer 21

64

Answer 22

Awesome Is it clear to you now ?

Answer 23

oh you know what I just remembered that \[\sqrt[2]{?}\] is the same thing as saying \[(?)\frac{ 1 }{ 2 }\]

Answer 24

yes correct you are right it would be ? ^ ( 1/2 )

Answer 25

so you just converted to a format that you could use... lolz

Answer 26

yes Is it clear now ?

Answer 27

yeah, thanks for explaining it to me.

Answer 28

You are most welcome :)