1. What do you think of when you hear the word “exponents”?

What is the difference between 3(2) and 3^2 ?

2. What is -(-3)^3? Write it out in long hand.

3. What is -2^5 and how does it compare to (-2)^5?

4. What does 3^-4 mean? Is your answer negative?

5. What does x^4 mean? What operation are you doing?

Define) Exponent
Define) base
Define) Standard form

1 answer

1. When I hear the word "exponents," I think of mathematical symbols that indicate the multiplication of a number by itself a certain number of times.

The difference between 3(2) and 3^2 is that 3(2) represents multiplying 3 by 2, which equals 6. On the other hand, 3^2 represents raising 3 to the power of 2, which means multiplying 3 by itself, resulting in 9.

2. -(-3)^3 can be written out in long hand as -(-3)(-3)(-3). This would be simplified as -(-3)(-3)(-3) = -(-27) = 27.

3. -2^5 represents raising -2 to the power of 5. This means multiplying -2 by itself 5 times. Therefore, -2^5 is equal to -32. On the other hand, (-2)^5 represents raising -2 to the power of 5, but the negative sign is included in the base. This means multiplying -2 by itself 5 times. Therefore, (-2)^5 is equal to -32.

4. 3^-4 represents raising 3 to the power of -4. This means taking the reciprocal of 3^4. Therefore, 3^-4 is equal to 1/3^4, which simplifies to 1/81. No, the answer is not negative.

5. x^4 represents raising the variable x to the power of 4. This means multiplying x by itself 4 times. This is an exponentiation operation.

Definitions:
- Exponent: A mathematical symbol that indicates the number of times a base is multiplied by itself.
- Base: The number or variable that is being multiplied by itself a certain number of times.
- Standard form: A number written in the conventional format using digits, decimal points, and decimal places, without any special symbols or notations.