No, an exponent is not called a base number.
the base is the number before the exponent: 34. 3 is the base, 4 is the exponent
the expont could also be refered to as three to the fourth power
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The base.
The base is the repeated factor, the exponent is the number of times by which the base is mutltiplied by itself. The exponent is also known as the power, althought the product of the exponential expression can also be described as the power.
the base
it is called an exponential form
If you have ab then a is the base and b the exponent