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.
_____
⁵√x¹⁰y¹⁵

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 sixth rut of P raised to the 36th Q raised to the 42nd. And our answer choices are answer choice. A the third rut of PQ squared answer choice B P raced to the 30th. Q raced to the 36th answer choice CP raise to the sixth Q raise to the seventh answer choice. DP raised to the seventh Q raised to the sixth. We look at our expression and we note from previous lessons that whenever we have a radical, we can rewrite this expression with rational exponents. So we take what's inside the radical? In this case, P raised to the 36th and Q raised to the 42nd and we rewrite these with rational exponents. The 36 and the 42 become the numerators in our rational exponents. And those are divided by our new denominator is the rut of the original expression. So in this case, six, so P is raised to the 36 6th. Well, we can reduce 36 6th. That's 36 divided by six, which is six. So we have P raised to the sixth power for Q being raised to the 42 6th. We can again reduce 42 6th. That's 42 divided by six, which is seven. So we have Q raised to the seventh power and P to the sixth Q to the seventh as is as reduced as this expression gets, We look at our answer choices and this matches with answer choice. C 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. _____ ⁵√x¹⁰y¹⁵