Whole number exponents are easy to explain. If n is any number and x is the exponent n^x means n multiplied by itself x times. When x is1 n^x=n, the number itself. But when x is zero, what does that mean? It always means 1, no matter what the number is, n^0=1.
And x can be negative. A negative exponent means we invert the number (eciprocal), so n^-2 means 1/n^2.
What about x equal to a fraction? Yes, that's possible, too. n^½ means the square root of n. And we can have any fraction for an exponent. This leads on to the concept of logarithms. When we multiply n^a by n^b we get n^(a=b). When we divide n^a by n^b we subtract exponents: n^(a-b). This enables us to do multiplication and division using addition and subtraction, which are easier to work with. We add and subtract exponents.
The subject gets quite involved, but that's the power of exponents!