5 Problems - SHOW ALL WORK!
1 . What does x^4 mean? What operation are you doing?
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 . What do you think of when you hear the word “exponents”?
What is the difference between 3(2) and 3^2 ?
1. x^4 means x raised to the power of 4. The operation being done is exponentiation, where x is multiplied by itself 4 times.
2. 3^-4 means 1 divided by 3 raised to the power of 4. The answer is 1/81, which is positive.
3. -2^5 means -2 raised to the power of 5. The answer is -32.
(-2)^5 means -2 multiplied by itself 5 times. The answer is -32 as well.
4. -(-3)^3 means the negation of (-3) raised to the power of 3.
(-3)^3 means -3 multiplied by itself 3 times, which is -27. Thus, -(-3)^3 is -(-27), which equals 27.
5. When I hear the word "exponents," I think of mathematical expressions where a number or variable is raised to a certain power. Exponents represent repeated multiplication.
The difference between 3(2) and 3^2 is that 3(2) means multiplying 3 by 2, which equals 6. On the other hand, 3^2 means 3 raised to the power of 2, which is calculated as 3 multiplied by itself, resulting in 9.