1. ## INDICES

a) express 27 to the power of a 1/2 as a power of 3

b) express root 2 as a power of 8

c) express root 2 divided by 16 as a power of 2

how exactly do you go about these Q's and what does it mean by expressing something as a power of something else? thanks

2. Originally Posted by abey_27
a) express 27 to the power of a 1/2 as a power of 3

b) express root 2 as a power of 8

c) express root 2 divided by 16 as a power of 2

how exactly do you go about these Q's and what does it mean by expressing something as a power of something else? thanks
expressing something to the power just means transforming the given number into a number, say x, raised to a power, say y...if that makes any sense lol

so for a) the question is asking you to express 27^1/2 as a number raised to a power i.e. x^y. here you have been given x as 3.

so 27^1/2 is the same as (3^3)^1/2 which is the same as 3^(3^2)

sorry dont know how to type in mathematical equations but if you write the above on paper, hopefully it will make sense.

3. b) express root 2 as a power of 8

this question is saying: root 2= 8 to the power something

now we need to find this something...let's call it x

so root 2 = 8^x

remember root 2 is the same as 2^(1/2) and 8 is the same as 2^3

so 2^(1/2)=(2^3)^x

then equate indices:

so 1/2 = 3x
so x = 1/6

so root 2 = 8 to the power 1/6

4. right the first seems rather straight foward now, but what about c), how do you deal with roots as a numberator, as in root 2 over 16?? thanks

Originally Posted by thegarden
expressing something to the power just means transforming the given number into a number, say x, raised to a power, say y...if that makes any sense lol

so for a) the question is asking you to express 27^1/2 as a number raised to a power i.e. x^y. here you have been given x as 3.

so 27^1/2 is the same as (3^3)^1/2 which is the same as 3^(3^2)

sorry dont know how to type in mathematical equations but if you write the above on paper, hopefully it will make sense.

5. c) express root 2 divided by 16 as a power of 2

the question is saying: root2 divided by 16 =2^x, we need to find x

keeping in mind that root 2 is the same as 2^(1/2) and 16 is the same as 2^4

so 2^(1/2) divided by 2^4 = 2^(-7/2)...cos we know that when we divided powers we have to take away

going back to the question...2^(-7/2)=2^x

to find x, we equate indices, so -7/2=x......so x=-7/2

Therefore, root 2 divided by 16 = 2^(-7/2)