The exponential form is a shortcut way of writing multiplications by the same number that is repeated. To write 5^6, in exponential form, one would write 5 x 5 x 5 x 5 x 5 x 5.
It is really important when writing longer multiplications like 11 ^ 12, which in exponential form, could simply be written as 11 x 11 x 11 x 11 x 11 x 11 x 11 x 11 x 11 x 11 x 11 x 11. The exponent is the number of times the number is written in multiplication. In the examples provided, 6 and 12 are the exponents, while 5 and 11 are the bases.