Final answer:
The expression 6 * 3^10 + 3^11 simplifies to 7 * 3^10 because we combine the like terms with exponents, using the rule of exponent addition for the same base.
Step-by-step explanation:
To solve the problem 6 * 3^10 + 3^11, we need to apply the laws of exponents that relate to multiplying powers with the same base. When we multiply like bases, we add the exponents. Since 3^11 is the same as 3^1 * 3^10, we can see that 6 * 3^10 + 3^11 is equivalent to 6 * 3^10 + 1 * 3^10, which combined is 7 * 3^10.
Thus, this expression simplifies to a single power of 3. We know that 7 is not a power of 3, but in this problem, 7 is just a coefficient multiplied by 3^10. Therefore, the expression does not simplify to a cleaner power of 3, but rather stays as 7 times the 10th power of 3 (7 * 3^10).