to the power of a fraction

[mollykins]

When working out the value of a number to the power of a fraction, I was always told to root by the bottom number then times it by itself by the numerator. But does it always work if you do it in the opposite order?

For example 4 ^ 3/2, you could say the sqrt of 4 is 2, 2^3 is 8. OR 4^3 is 64, and the sqrt of 64 is 8.

Do all work this way, as long as the numerator is the thing you do to the power of and the denominator is the root? If so, in exam conditions, you want to find the quickest and easier way to do something, so if you have one of the numbers of the fraction as something higher than 3, it would be easiest to do that bit as the one you do tothe power of, rather than working out the 4th root of something.

[gen2]

I confirm that you are correct, the order doesn't matter between these two operators.

Similarly, multiply and divide can be done in either order ( and also + and -)

[mollykins]

I asked Niamh (my cousin) who wasn't sure but she says the order probably doesn't matter for either but you have to be careful incase the answer would be just +ive or positive or negative!