Evaluate the following expression. ( − 4 ) 4 \left(-4\right)^4

Here we're asked to evaluate the following expression. We're given here the exponential expression negative four raised to the power of four. So this is an exponential expression with a negative base. Now remember that regardless of if our base is negative or not, exponents always indicate repeated multiplication. So negative four to the fourth power is simply negative four multiplied by itself four times. So negative four times negative four times negative four times negative four. I'm gonna go ahead and pair these off to make this multiplication a bit more manageable. Four negative four times negative four will give me positive 16. Then another pairing of negative four times negative four will give me another positive 16. So I have 16 times 16, which gives me 256. Now a last check when we're dealing with exponential expressions that do have a negative base is to think about whether we expected our final answer to be positive or negative. Here, I have a negative base raised to an even exponent, which tells me that I should end up with a positive value. And I did here positive at 256. Let us know if you have questions and let's keep going.