Maths question - help needed please

[Huggybear16]

I am struggling with part (b) to this question.

I know that (a) is 81, but I have no idea how to work out the answer to part (b).

Can someone please explain to me, baby step by baby step, how to work out the answer? It is a non-calculator paper.

Many thanks

27 is 3 to the power of 3 (3 cubed), so x is 3.

In terms of working it out, GCSE pupils are expected to recognise 27 as 3 cubed.

Oh sorry - missed the square root sign. Give me a sec.

But it's the root of 27, not 27. The answer is 3/2, but don't know how that is calculated.

Another way to write the square root is as 27 to the power 1/2
As the pp pointed out 27 is 3 to the power 3
Now multiply the powers gives you ^
f(x)^ is 3 to the power 3/2 (or 1.5) so x is 1.5

Square both sides - gives you 3 ^2x = 27
So 2x = 3 by the earlier logic

So the square root of 27 is 27 to the power of 1/2.

3 has been raised to the power of 3, then this has been square rooted (raised to the power of 1/2).

Using index laws (I can try to explain further if needed on this) this can be done in one step by multiplying 3 by 1/2, which is 3/2 or 1.5. So x is 1.5.

It's about understanding the Laws of Indices:

3^x = root 27
3 cubed is 27 and that can be written as 3^3
You want the square root of 27 which can be written to the power of 1/2
So the square root of 27 is 3^(3/2)

Sorry - my laptop doesn't lend itself to setting this out nicely but hope that helps a bit

Too slow typing!

multiple cross posts!

this may help though

www.bbc.com/bitesize/guides/zpkmpbk/revision/7

Thank you all.

I'm just trying to really understand how to get this.

3x = 270.5 I get

To get from 3 to 27, you cube it. So to get from 3 to 27^0.5, you "half cube it" hence 1.5?

Yes! That bitesize page will absolutely help. Thank you.

I will try more problems tonight when I get home and see how I get on. I may post again if I get stuck if you all don't mind.

I would rewrite 27 as 33. Then use the index law (xm)n = xmn and rewrite the rhs as (33)(1/2) since the square root of a number is to the power of (1/3) .
Then using the index law above, 3x1/2 = 3/2

Sorry, that should've townthe power of 1/2 not 1/3.

Actually @xsquared that does make sense to me, and is actually ringing some bells now. Everyone's explanation actually rings a bell, just trying to remember the way I use to do it.

I did all this around 17 years ago and hugely underestimated how much I'd forgotten.

My problem is that I can't picture it. I can picture a³ as a x a x a but I can't picture a‐³ or a½. At the moment, negative or fraction indices just aren't making sense to me.

I'm going to work through that bitesize pages and try to find more questions to try tonight.

Hope this helps.

It does help! I really do need every step written, just like you have there. Even when I am answering questions, I need to write down everything. Thanks very much.