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

Question

2. What does 3^-4 mean? Is your answer negative?
3. What is -2^5 and how does it compare to (-2)^5?
4. What is -(-3)^3? Write it out in long hand.
5. part A)What do you think of when you hear the word “exponents”?
part b) What is the difference between 3(2) and 3^2 ?

Answer 1

1. x^4 means raising the variable x to the power of 4. The operation being done is exponentiation.
2. 3^-4 means raising the number 3 to the power of -4. The answer is not negative, but rather a positive fraction, 1/81.
3. -2^5 means raising the number -2 to the power of 5. The answer is -32. (-2)^5 means raising the number -2, enclosed in parentheses, to the power of 5. The answer is -32 as well. So, in this case, there is no difference.
4. -(-3)^3 can be solved step by step as follows:
-(-3)^3 = -( (-3) * (-3) * (-3) )
= -( -27 )
= 27
5. a) When I hear the word "exponents," I think of the process of multiplying a number by itself a specific number of times.
b) The expression 3(2) means multiplying 3 by 2, which equals 6. On the other hand, 3^2 means raising 3 to the power of 2, which is equivalent to 3 multiplied by itself, resulting in 9. So, the difference is that 3(2) is a multiplication operation, while 3^2 is an exponentiation operation.