Final answer:
The expression 7x7x7x7x7x7 can be succinctly written as 7^6 in exponential form, obeying the mathematical rule where (x^a)^b equals x to the power of a times b (x^(a.b)).
Step-by-step explanation:
The expression for 7x7x7x7x7x7 can be written in exponential form as 76. When you have a repeated multiplication of the same number, you can use exponents to express this more concisely. The base number is 7 and the exponent is 6 because 7 is multiplied by itself six times. This follows the mathematical rule of exponents where (xa)b = xa.b.
Another example to clarify this rule is with the number 5. If you think of (53) as (5 × 5 × 5)4, you would end up multiplying 5 by itself 12 times, which is 512. This demonstrates how the exponents are multiplied when one exponent is raised to the power of another.