Is there a difference between -74 and (-7)4? Read through each expansion shown below. Notice the difference when using parenthesis vs. not using parenthesis.
-74 = (-1)(74) = (-1)(7)(7)(7)(7) = - 2401
(-7)4 = (-7)(-7)(-7)(-7) = 2401
Remember, a negative times a positive gives a negative, but a negative times a negative gives a positive. So this makes a big difference!
Explanation
Practice #1
Practice #2
| -52 -5·5 = -25 |
The exponent only applies to the number or variable to which it is attached. In this example, -52, means the negative of 5 squared. We square 5 and then make the answer negative. |
| (-5)2 (-5)(-5) = 25 |
In this example, we are asked to raise -5 to the second power. (-5)2 tells us to multiply -5 times -5. The answer is positive because a negative times a negative is positive. |
| -(-5)2 -(-5)2 =(-1)(-5)(-5) =(-1)(25) = -25 |
-(-5)2 asks us to square the -5 then multiply that by -1. |
Can you tell the difference between -1(3) and (-3)? Click the Practice 1 and 2 tabs to try two practice problems and find out!
What is -32?
(-1)(3)(3)= - 9 The exponent tells you to square 3. Then the negative sign tells you to multiply by -1. The answer is negative 9.
What is (-3)2?
(-3)(-3)=9 The negative sign is inside the ( ) so we square the negative 3. A negative times a negative is positive, so the answer is positive 9.
