Last minute maths homework help please mners!

[MrsFogi]

DD is stuck, I am stuck (but I'm not going to let on that I'm stuck because I don't want her to even think that maybe I'm not amazing at maths and that it might not be my favourite thing - so I'm "mulling it over") - can you help me "magically" be able to do this and explain it?

Simplify 6 (to the power of 8 i.e. a little 8 above the 6 that I can't do on the mn site) x 6 (squared i.e. a little 2 above the 6) without using a calculator. Give your answer as a power of 6.

So I know that 6 squared means 6x6 so 36.
How on earth do I do 6 to the power of 8 - do I have to do 6x6 then 36x6 then product of that x6 and so on for the rest of the evening? Or does it work to multiply the little 8 by the little 2 or add them? And then what does to the power of 6 mean? [no idea emoticon] [please enlighten me emoticon].

You can use the product rule as they have the same base (6)

So all you need to do is add the two powers.

8 + 2 = 10

So it's 6 to the power 10

Yes, just add the indices as said above.

Well it's 66 +66666666
If you count the 6s there are 10 so 6 to the power of 10.

As above but to explain why:

6 to power 8 = 6x6x6x6x6x6x6x6
6 squared = 6x6

So taking the two together, you have 6x6x6x6x6x6x6x6 x 6x6 which is 6 to the power 10.

To try and explain:
It's (6x6x6x6x6x6x6x6) x (6x6)

If you multiplied that all out you'd get
(6x6x6x6x6x6x6x6x6x6)
As you're multiplying your first set of brackets by the first six, then that number by the second six.

Can't tell if I've explained this well enough or will have made it more confusing.

Oops! Hasn't seen this was already explained while I was busy counting 6's on my phone

If you wrote it as 6 x 6 x 6 ... 10 times then you can show why the answer is 6^10 as it's eight 6s multiplied by 2 more 6s so 10 altogether (depending how old DD is she may not have done the rules of indices before).

www.khanacademy.org/math/in-eighth-grade-math/exponents-powers-1/laws-exponents/v/exponent-rules-part-1

Thank you to all who replied - yet again you lovely mathematically minded mners have saved me and I have successfully passed myself of as having worked it out overnight . Thank you!