Indices and Roots

[MuddledMaths]

Hey, Can someone explain how you simplify something like 16/√2 (sixteen over root two) into a power of 2?
The answer is 2 to the power of 1/8 but I'm not sure how you get that.
Thanks in advance and sorry for bothering anyone, I know it might be a stupid question, but I just don't get it.

 

[blamocur]

Hey, Can someone explain how you simplify something like 16/√2 (sixteen over root two) into a power of 2?
The answer is 2 to the power of 1/8 but I'm not sure how you get that.
Thanks in advance and sorry for bothering anyone, I know it might be a stupid question, but I just don't get it.

I am not sure how one can get [imath]2^{1/8}[/imath] since it is a wrong answer.

But to get it right: you have a fraction where both numerator and denominator are powers of two -- do you know how to divide powers with the same base?

 

[pka]

Hey, Can someone explain how you simplify something like 16/√2 (sixteen over root two) into a power of 2?
The answer is 2 to the power of 1/8 but I'm not sure how you get that.
Thanks in advance and sorry for bothering anyone, I know it might be a stupid question, but I just don't get it.

Can you manage basic operations? [imath]16=2^4~\&~\sqrt{2}=2^{\tfrac{1}{2}}[/imath]

[imath][/imath]

 

[MuddledMaths]

Can you manage basic operations? [imath]16=2^4~\&~\sqrt{2}=2^{\tfrac{1}{2}}[/imath]

[imath][/imath]

Yes

 

[MuddledMaths]

I am not sure how one can get [imath]2^{1/8}[/imath] since it is a wrong answer.

But to get it right: you have a fraction where both numerator and denominator are powers of two -- do you know how to divide powers with the same base?

Dont you then subtract the powers if the base is same? Like 10^4 / 10^2 = 10^2

 

[MuddledMaths]

Can you manage basic operations? [imath]16=2^4~\&~\sqrt{2}=2^{\tfrac{1}{2}}[/imath]

[imath][/imath]

We just started doing them

 

[Deleted member 4993]

Dont you then subtract the powers if the base is same? Like 10^4 / 10^2 = 10^2

Yes - then

\(\displaystyle \frac{16}{\sqrt{2}} \ = \ \frac{2^4}{2^{\frac{1}{2}}} \ \) .......... continue

 

[pka]

We just started doing them

Do you know about the rules for exponents? When to add? When to subtract?

 

[MuddledMaths]

Do you know about the rules for exponents? When to add? When to subtract?

We have all the laws in our notes, just not familiar enough to know them off the top of our heads

We have all the laws in our notes, just not familiar enough to know them off the top of our heads

But sort of ya

Yes - then

\(\displaystyle \frac{16}{\sqrt{2}} \ = \ \frac{2^4}{2^{\frac{1}{2}}} \ \) .......... continue

Oh. So then 4 - ½ = 3½
Ans- 2^3½

 

[Dr.Peterson]

Oh. So then 4 - ½ = 3½
Ans- 2^3½

But since we generally avoid mixed numbers in algebra, rewrite [imath]3\frac{1}{2}[/imath] as a single fraction ... and it will look more like the wrong "answer" you gave initially.

 

[Steven G]

The rules you are referring, imo, should NOT be memorized. They should be easily seen in your head.

For example 2³ by definition means 2*2*2, while 2⁵ by definition means 2*2*2*2*2.
So 2³*2⁵ = (by definition) [2*2*2][2*2*2*2*2] = 2*2*2*2*2*2*2*2 = 2⁸. Do you see the addition staring you in the face?

Now 2⁵/2³ (2*2*2*2*2)/(2*2*2) = 2*2=2². Do you see the two 2's canceling out?

 

[MuddledMaths]

But since we generally avoid mixed numbers in algebra, rewrite [imath]3\frac{1}{2}[/imath] as a single fraction ... and it will look more like the wrong "answer" you gave initially.

Then 7/2

 

[MuddledMaths]

So for 8√2 how would you figure it out or do you just learn them kinda?

So for 8√2 how would you figure it out or do you just learn them kinda?

Sorry

 

[Steven G]

Hint: 8=2³ and √2 = 2^1/2

 

[JeffM]

We have all the laws in our notes, just not familiar enough to know them off the top of our heads


But sort of ya


Oh. So then 4 - ½ = 3½
Ans- 2^3½

But sort of??????????????????

You can figure everything out from

[math]\text {For all } r > 0, r^0 = 1, \ r^a * r^b = r^{a+b}, \ r^a \div r^b = r^{a-b}, \ \sqrt[b]{r^a} = r^{a/b}. [/math]

 

[MuddledMaths]

I mean after the chapter and practicing the sums in exam papers we would be more familiar with them to be able to know which rules to use by just looking at the sum. We still need a little more help on things like equations involving indices because our teacher moves very fast through chapters. Our laws are in a different format but they are the same:

 

[MuddledMaths]

We just need a minute to understand which law to use cause we literally just started the chapter

 

[MuddledMaths]

Hint: 8=2³ and √2 = 2^1/2

So 8√2=2^7/2

 

[Deleted member 4993]

So 8√2=2^7/2

8√2=2^(7/2) ............... those parentheses are NEEDED to distinguish the result from \(\displaystyle \frac{2^7}{2}\)

 

[MuddledMaths]

Ya sorry, I'm just typing on a phone sso I wasn't sure how to represent that