Final answer:
To simplify the expression 734 to the power of 2 times 734 to the power of 8, you add the exponents together because the bases are the same, resulting in 734 to the power of 10.
Step-by-step explanation:
The problem given requires us to simplify the expression by using exponent rules for multiplication. The rule states that when we multiply two exponents with the same base, we can add the exponents together. Therefore, for the expression 7342 × 7348, we add the exponents 2 and 8 to get 7342+8, which simplifies to 73410.
This process of simplifying exponentials is essential in algebra and precalculus, and understanding it can significantly reduce the complexity of equations. The underlying principle is that the exponents are merely shorthand for repeated multiplication, so when the bases are the same, the multiplication operation translates to adding exponents.