In Exercises 1–20, use radical notation to rewrite each expressio...

Question

In Exercises 1–20, use radical notation to rewrite each expression. Simplify, if possible.

(-27)^⅓

Accepted Answer

Hey, everyone in this problem, we're asked to write the given expression in radical notation. And to write the answer in simplified form, the expression we given is negative 64 to the exponent one third, we have four answer choices. Option A, the third route of negative 64 or four. Option B, the third route of negative 64 or negative four. Option C the third route of negative or negative 64 divided by three. And option D, the square root of negative 64 Q or negative four, we're gonna start by rewriting what we were given. So we have a -64 to the exponent 1/3. Now we're asked to write this in radical notation. So let's recall the relationship between exponents and radicals. If we have a, to the exponent one divided by N, this is equal to the nth root of A. OK. So we can transform our exponent into a radical and vice versa. In this case, we have negative 64 as the base of our exponent. So our a value is negative 64, our exponent is one third. OK? One divided by three. And so our end value is three. So if we apply the rule to this expression, we get that this is equal to the third route or the cube route Of -64. So now we have our radical notation and we want to simplify, we wanna take the cube root of a number. So what we're trying to do is find a number where when we raise it to the exponent three, we get -64. Well, we know that negative four cubed gives us negative 64. So we can write this as the cube root of negative four cubed. We have the cube root of something cubed. So this is just equal to negative four. OK. Those two cancel each other up. So we found our expression written in a radical notation and then we simplified to get a single numeric value for this expression. The correct answer is the Q root of -64, which is equal to -4. This corresponds with answer choice B. Thanks everyone for watching. I hope this video helped see you in the next one.

In Exercises 1–20, use radical notation to rewrite each expression. Simplify, if possible. (-27)^⅓

Key Concepts

Radical Notation

Cube Root

Simplification of Radicals

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