In Exercises 79–112, use rational exponents to simplify each expr...

Question

In Exercises 79–112, use rational exponents to simplify each expression. If rational exponents appear after simplifying, write the answer in radical notation. Assume that all variables represent positive numbers.
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³√8a⁶

Accepted Answer

Welcome back. I am so glad you're here. We're asked to further simplify the following expression. Noting that any variable that appears in the expression represents positive numbers. The expression we're given is the third rut of 27 P raised to the 9th. Our answer choices are answer choice A nine P squared answer choice B three P squid answer choice C nine P cubed and answer choice D three P cubed, right? Taking a look at our expression. There are several ways to go about simplifying this. I want to look at this as we recall from previous lessons that when we have the cubed root of two terms inside of there, we could set that equal to the cubed root of each of those two terms being multiplied together. So we have the cubed root of 27. That's not a 27. The cubed rot of 27 multiplied by the cubed root of P race to the 9th power because looking at the cubed root of 27, we know what the cubed root of 27 is what multiplied by what multiplied by what or what multiplied by itself three times equals 27 that's three. So we know that reduces to three. But now taking a look at the cube of P raised to the ninth power. We recall from previous lessons that when we have something written as a radical, we can rewrite that as a rational exponent. So we can take what's inside the radical. We've got this P and then that will be raised to an exponent. The numerator of the exponent is going to be the exponent from the original expression the 9th, that will be its numerator and nine is divided by the rot from the previous expression. That's going to be three, that will be our denominator. So we have P raised to the nine thirds and we can take nine thirds and simplify that nine thirds is the same as nine divided by three and nine divided by three is three. So we have three P cubed and that's as simplified as this one is going to get, we look at our answer choices and this matches with answer choice. D well done. We'll catch you on the next one.

In Exercises 79–112, use rational exponents to simplify each expression. If rational exponents appear after simplifying, write the answer in radical notation. Assume that all variables represent positive numbers. ___ ³√8a⁶

Key Concepts

Rational Exponents

Radical Notation

Simplifying Expressions

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