How would you write 6 × 6 × 6 × 6 as an exponential expression?

The answer is 6⁴.

Exponent is the number of times the factor is being multiplied. For example:
x * x = x²
x * x * x = x³
x * x * x * x = x⁴

So: 
6 * 6 * 6 *6 = 6⁴