Write ∛64 using exponents and evaluate.

Question

Accepted Answer

Hello. Everyone in this video we're going to be looking at this practice problem where we want to write the expression the cubed root of as in exponential form and then evaluate so whenever you have radicals you can express them as variables. Where you can express them as exponents with fractions. So in this case say I have X. To the power of M divided by N. I can rewrite this as a radical. Where my denominator N is the route I'll be taking. So I'll be taking the end route of X. But to the power of my numerator M. So notice how I started with a fraction in my exponent. But I ended up writing it as a radical. So we're going to use this sort of rule to help us evaluate the cubed root of 1728 as an exponent. So in this case you can see that has a exponent of one. So if I were to convert this into exponential form I pull out The number inside the radical which is 1728 and now my denominator is the route I was taking. So in this case I was taking the third route. So that becomes my denominator for my fraction. And as we said before 1,728 had a power of one inside the radical which means I'm left with 1, to the power of one third when I write it in exponential form and now we need to evaluate this expression. So we can evaluate by Knowing the cubed root of 1728. But if we don't know the cubed root of we can break down Into its factors. So I can say this is the same as 144 times and 144 is the same as 12 times 12. I still have this 12 this 3rd 12. So this becomes 12 to the third. So I can say that 12 to the third is equal to 1728. And I can actually plug this in to this expression here. So if I do that I now have 12 to the third inside parentheses to the power of one third. And because this one third is on the outside of the parentheses I can multiply that in To the exponents on the inside of the parentheses which in this case is three. So this will become 12 to the power of three times 1/3. And that's equal to 12 to the power of three divided by three or just 12 to the first power. So when I evaluate it I got 12. So if I rewrite an exponential form I have 1, to the one third power. If I evaluate it I get 12 these are my final answers for this problem and you can see that it aligns with answer choice B. So hopefully this video helped and see you next time.

Write ∛64 using exponents and evaluate.

Key Concepts

Radicals and Exponents

Evaluating Cube Roots

Properties of Exponents

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