Evaluate 125 to the power of a third.
In order to actually solve this problem, we’ll first want to have a look at the exponent. And we have a third. So what does this mean? We actually have an exponent rule. And this tells us that 𝑥 to the power of one over 𝑎 is equal to the 𝑎th root of 𝑥.
For example, if we had 𝑥 to the power of a half, this would be equal to the square root of 𝑥. Or if we had 16 to the power of a quarter, this would be equal to the fourth root of 16. Okay, great! So now we know what this means. So let’s actually rewrite our term.
So we can say that 125 to power of a third is equal to the cube root of 125. So therefore, the answer is going to be five. And this is because five multiplied by five multiplied by five is 125, because we get five multiplied by five is 25, 25 multiplied by five is 125. So therefore, we can say that 125 to the power of a third is equal to five.