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.
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