Algebra Practice Test

What is the simplified exponential notation for a • a • a?

1. a^2

2. a^3

3. 3a

4. a^4

The correct answer is: a^3

The expression a • a • a represents the multiplication of the variable 'a' by itself three times. In exponential notation, this is expressed as 'a' raised to the power of the number of times it is multiplied by itself. Since the variable 'a' appears three times in the multiplication, the correct simplified form in exponential notation is a^3. This indicates that 'a' is being multiplied by itself three times, which directly corresponds to the definition of exponents. The other options do not accurately reflect the multiplication of 'a' three times. For instance, while a^2 would indicate 'a' multiplied by itself two times, and a^4 would indicate it multiplied by itself four times, both do not match the three instances present in the question. The option 3a suggests adding three 'a's together rather than multiplying them, which is also not the intent of the original expression. Thus, the option a^3 accurately captures the essence of multiplying 'a' by itself three times.