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Lesson 5: More on order of operations

# Comparing exponent expressions

In this math activity, we arrange three math expressions from smallest to largest. We evaluate the expressions: 2 cubed minus 2, 2 squared plus 3 to the power of 0, and 3 squared. We find their values to be 6, 5, and 9. The correct order is 5, 6, and 9.

## Want to join the conversation?

• My main question is why is anything to the power of 0 equal to 1?(I watched the videos a lot but still don't understand.I even PAY ATTENTION.)
• I like to think of it this way. 2^0 can be answered as 1 multiplied by two, zero times. The number one is not being multiplied by anything, not even the number zero. So the answer is the number one (1).
• Sal:Here we have 3 to the 0th power, which is clearly equal to 1.
Me, thinking that anything to the 0th power is 0: ...Clearly?
• yes because sal did used the 1st method as said in intro to exponents
• i keep thinking that 3 to the power of 0 is 3 but i know its not but keep forgeting that its 1 how is it 1?
• It is because exponents represent repeated multiplication. Anything to the power of 0 equals 1. This ultimately means that the value always ends up being divided the same amount of times it was multiplied. 3^0 means, after you multiply by 3 a specific number of times, you are going to have to divide by 3 the same number of times. So regardless of whether you get to multiply by 3 one time, two times, dozens of times, hundreds of times, thousands of times, trillions of times, or even so many times that we can not imagine, every multiple is instantly removed and the only factor that remains is 1.
• is 0^0= undefined? or just 0
• it is going to be 0 because 0 to the first power is 0 and to the 2nd power also 0
• Hi,
On a different video, Sal says that 0 raised to the power of 0 is left undefined. In this video, he says it equals 1. Did he just pick it? Was it specified in the question?
• It depends on who you talk to. Some people say that 0^0 is 1, some people say it’s 0, and some people say it’s undefined. The most common thing I’ve heard people say is that 0^0 is 1. If you put this into a calculator, then it will say 1. (I know Google and the Khan Academy calculators say this)
• anything to the power of 0 equal to 1?
• With the exception of 0^0 which is indeterminate
• I am not understanding the logic of 3 to the zero power = 1.
The way my brain works is taking 3 and multiplying it by itself 0 times, which would equal 3. Where do we get 1 from? Is it just a rule that we should know when to apply?
• Anything to the power of zero (except 0) will equal 1 because exponents are repeated multiplication, and a power of 0 means the value was multiplied by itself 0 times. Since anything times 1 equals itself, after we "factor out all the multiples" the final value we will be left with is a 1.