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.

81^3/2

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 are given is 64 to the exponent 3/2. We have four answer choices. Option A, the square root of 64 cubed or 64. Option B the cube route of 64 or 8. Option C the cube root of 64 squared or 512. In option D, the square root of 64 cubed or 512, we're gonna start by rewriting the expression we were given, we have 64 to the exponent 3/2. We want to write this in radical notation. Well, we don't have a girl for dealing with kind of mixed numbers like we have here in our exponent. There's 3/2. OK? So let's try to break this exponent up. Recall, we have a rule that says if we have a to the exponent M multiplied by N, we can write this as a to the exponent M to the exponent end. So if for exponent is some values multiplied together, we can break those up into an exponent of an exponent. In our case, we have an exponent of 3/2, but notice 3/2 is equal to one half multiplied by three. So the exponent is two things multiplied together. It's the product of these two numbers. And so we can write it as an exponent of an exponent. We can write this as 64 to the exponent 1/ all to the exponent three, no working inside the inside bracket. And we have an exponent of one half. We wanna write this in radical notation. We recall that if we have a to the exponent one divided by N, this is equal to the end through of A. In our case, we have an exponent of 1/2 the one divided by two. So this is equivalent to the square root. So we can write this as the square root of 64. Cute. So we have our simplified expression in radical notation, the square root of 64 cubed. So we know we're looking at answer choice either A or D. Now let's figure out what this evaluates to. We know that the square of 64 is 8. So in our brackets, we have eight cubed, an eight cubed is equal to 512. So we have our expression that we found in radical notation, we simplified it to get a single value. And we found that we had the square root of 64 all cubed or 512 this corresponds with answer choice D. 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. 81^3/2

Key Concepts

Radical Notation

Exponents and Fractional Exponents

Simplification of Expressions

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