# law of indices problem

• Nov 16th 2012, 02:37 AM
CuriousChris
law of indices problem
Hi

The name is Chris, I am the father of a boy in year 11. My maths classes were many years ago and I only ever got to year 10 :(

Can you help me help him?

he has the following problem

9x+1/32x-1 find to the power of 3

Now I know the answer is 33 but I need to understand the steps to get to it
That way I can work through it with him

I know it must be simple as wolframalpha doesnt even bother showing the steps

• Nov 16th 2012, 03:08 AM
chiro
Re: law of indices problem
Hey CuriousChris.

The basic reason is that 3^2 = 9 and power laws work in that (x^a)^b = x^(ab) so if you let x = 3 a = 2 and b = x+1 then (3^2)^(x+1) = 3^(2(x+1)) = 3^(2x+1) = 9^(x+1).

So if 3^(2x+2)/3^(2x-1) using exponent laws if you divide you subtract the bottom index from the top to get 3^(2x+2 - (2x-1)) = 3^(2+1) = 3^3.
• Nov 16th 2012, 09:50 AM
anthonye
Re: law of indices problem
In problems like this you have to make the bases the same so the 9 becomes 3^2 giving
3^(2x + 2) / 3^(2x - 1) then like chiro says using the second law of indices division become subtraction (when the bases match) giving

3^(2x + 2) - (2x - 1) = 3^(2 + 1) = 3^3 = 27.

Good luck.
• Nov 17th 2012, 01:38 PM
CuriousChris
Re: law of indices problem
Hi Guys this is my third attempt to reply. Sorry I keep getting dragged away.