Write 27^2/3 in radical form and evaluate.

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Accepted Answer

Hello. Everyone in this video we're going to be looking at this practice problem where we want to write 1296 to the 3/4 power in radical form and evaluate. So in this case you can see that we're going to be working with Radical Form. Not only because the question asked for it but because we also have this fraction in the exponent. So recall that whenever you have a fraction in the exponent you can rewrite it using you can rewrite the expression using a radical. So say I have for example A. To the power of M divided by N. I can rewrite this in radical form by saying I will be taking the N. Through of A. To the M. So in this case notice how the denominator and became the route I was taking and this numerator, M became the power that was being applied. So N was the denominator. So I'm taking the route of the variable A. But to the power of M the numerator. So we're going to use this rule to help us rewrite as a radical. So notice for 1296 3 is the Numerator and four is the denominator. So if I rewrite this in radical form I have the fourth route of 1296 To the power of three. So this would be rewriting 1296 : 3. 4th power in radical form. But if we want to evaluate it We have to think of 1296 as an ex one at first. So if we break down the factors of 1296 I can do 36 times 36. And I can also break this down further by saying six times six times six times six. And now we have 6 to the 4th power Is the same as 1200 96. And if I reapply this six to the 4th power into my original expression I can see 6 to the 4th power times the exponent three fourths You can see that now I can multiply 3/4 times four because the exponent is on the outside of the parentheses. So this becomes six to the power of four times three divided by four, That equals 6 to the power of 12 divided by four, While 12 divided by four is the same as three. So this is the same as six to the third power and 6 to the 3rd power is equal to 2 16. So you can either evaluate it by breaking down 1,296 as an exponent or you can also evaluate it using this sort of radical that we came up with either way works. But this becomes our final answer For the expression in radical form where we have the fourth root of 1, to the third power and if we evaluate that that is 216, you can see that that aligns with answer choice d. So hopefully this video helped and see you next time.

Write 27^2/3 in radical form and evaluate.

Verified Solution

Key Concepts

Exponents and Radicals

Order of Operations

Evaluating Expressions