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.
__
⁸√x²

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 that we're given is the 10th root of pray to the fourth power. Our answer choices are answer choice A the fifth rut of P squared. Answer choice B the square root of prays to the 5th power answer choice C the square root of P and answer choice D, the crate of P squared. All right, we recall from previous lessons that whenever we have an expression written with a radical, we can rewrite that with a rational exponent, we take what's inside of the radical. We've got this P variable here. And then the numerator of the rational exponent is going to be the exponent from the original expression. So that's going to be four and that's divided by the root from the original expression. That will be the denominator in this case 10. So we have P raised to the 4/10. Well, we look at 4/10 and we recognize that we can simplify that both four and 10 have a greatest common factor of two So we can divide both of them by two, four, divided by two is two. So we have two in the numerator that's divided by 10, divided by two, which is five. So P is raised to the 2/5. Now we can get this back into a radical expression. Again, the numerator is going to be the exponent for the P. So if P squared and that's still inside of a radical and the uh index of our radical will be the denominator of our rational exponent. And in this case, that's five. So we have the fifth root of P squared and that is as simplified as this expression gets, we look at our answer choices and this matches with answer choice a well done. We'll catch you on the next one.

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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. __ ⁸√x²