When working with exponents, is there any difference in operations if the exponents are whole numbers or fract

Question

I would appreciate any help. Thanks

Answer 1

no, it is the same:
a^{1/2} a^{1/2} = a{1/2+1/2} =a
(a^{1/3})^6= a^{6/3} = a^2 .

Answer 2

if the exponent are whole number you need to raise it to the power of the exponent but if it is a frac you should do the reversed which is take the root to the power of the exponent example 9^2=81 and 9^(1/2)=3 hope this helps

Answer 3

As long as the exponents are equivalent, then not at all.

For instance, let's take 5^2 (or "5 squared"). This is exactly the same as saying 5^(1 + 1), or 5^(4/2), or 5^(2cos(0)).

There's no difference.

Answer 4

No, but its an unusual concept to get used to. Basically, when you have something that looks like:

x^(1/y)

you're looking for the number which, when raised to the y power, is x.

Example:

128^(1/7) = z

So which number, z, when raised to the 7th power is 128?
(it's 2)

Remember this, if nothing else:

x^(1/2) = √(x)

It will help you understand the broader concept.

Answer 5

No. this is not. a similar guidelines of operation are observed for fraction exponents as for entire numbers. yet you should follow the guidelines for fractions-addition, fractions-subraction, fractions-multiplication, and fractions-branch.

Answer 6

Not at all...u can use anything
Real number,complex numbers and even u can use functions of variables
e^1
100^-1.5
2 ^ 5/2
e^ 8 - 6i
x^ a^2
5^ cosθ
e^csc²θ
etc.........

Answer 7

No not at all.