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    a) Evaluate 2^1 x 1^23 x 9^0
    the answer is 2.... why?

    b) (1 2/7)^2
    the answer is 1 ^ 32/49

    This would be much easier to understand if you used LaTeX to write your expressions.

    a) You probably know that indices are always done before multiplication, so you must work out each power before multiplying anything.
    2^1 = 2 as putting anything to the power of 1 does not change it at all.
    1^{23} = 1, as this just means 1 \times 1 \times 1 ... 23 times, which is obviously 1.
    9^0 = 1 as anything to the power 0 is 1.
    After that, you just have 2 \times 1 \times 1 which is obviously 2.

    b) I'm really not sure what you mean here, that would be 81/49.

    1 and 2/7 is the same as 9/7

    9/7 squared is 81/49

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