Final answer:
The question involves using the power rules for exponents to simplify (3n)². According to the power rules, the expression simplifies to 9n², by squaring each component of the term separately.
Step-by-step explanation:
The student has asked about applying the power rules for exponents, specifically using the example of (3n)². According to the power rules, when you raise a product to a power, you raise each factor in the product to that power. In this case, the expression (3n)² can be simplified by squaring both the coefficient 3 and the variable n separately. Hence, (3n)² becomes 3² × n², which simplifies to 9n² because 3 squared is 9 and n squared is n².
Here are some examples illustrating the rules of exponents:
- Cubing a term like 2³ involves cubing the number 2 and multiplying the exponent by 3 if there is one.
- For multiplying exponential terms such as 10³ × 10², we add the exponents resulting in 10^(3+2) or 10µ.
- Raising a number to a higher power, like n to the fourth power (n´), means multiplying n by itself four times.