Indices Problems

Taking a closer look at page 248 question 22:

(i) You are asked to express √2 as 2 to the power of something.
Remember that 9 to the power of ½ is the same as √9 which is = 3.
Make sure you know how to check this on your calculator.

(ii) Know your square and cube numbers.
Square numbers are 1,4,9,16,25,36,49,64,81,100,121,144,169,196 (up as far as 14²)
Cube numbers are 1,8,27,64,125,216 (up as far as 6³)
It is also useful to know your powers of 2.
2²=4, 2³=8 2^4 = 16 etc.

(iii)Looking at 8√2 you need to use your answers for the previous two parts to work this out. 8 = 2³ and √2 = 2 to the power of ½
So you need to apply the first rule of indices on the list on page 240, adding the two powers (even if one is a fraction).

Finally solving the equation.
Leave the LHS as it is.
Write down the RHS in the form that you arrived at in part (iii).
Now you have:
2 to the power of something (3x-1) = 2 to the power of something else (ans from part iii)
So you ignore the 2s and equate the powers to solve for x.

Note that you can check your answer by putting
2 ^ (3×x +1) into your calculator (subbing for x) and then check if you get the same result for 8√2.