Final answer:
The expression (x-8)^3(x-8)^4 can be rewritten as (x-8)^7 by applying the rule of exponents that allows the addition of exponents when multiplying exponentiated quantities with the same base.
Step-by-step explanation:
To rewrite the expression (x-8)^3(x-8)^4 applying rules of exponents, we can use the property that states when we multiply two exponents with the same base, we can add the exponents. Thus, we can rewrite the expression as:
(x-8)^(3+4) or simply (x-8)^7.
This is because the base, (x-8), is the same in both terms, so we're effectively multiplying it by itself 3 times and then 4 times more, which is the same as multiplying it by itself 7 times in total. This is an application of the power rule for exponents, which is a fundamental aspect of working with exponentiated quantities.