Simplify each expression. Write answers without negative exponent...

Question

Simplify each expression. Write answers without negative exponents. Assume all vari-ables represent positive real numbers. See Examples 8 and 9. (x^1/4y^2/5)^20/x^2

Accepted Answer

Welcome back. I am so glad you're here. We are given this expression in the numerator. We have P. Two, the 2/7 times Q to the 3/14. So and that's all raised to the 28th power and it's divided by P raised to the 5th. Power. Alright so we've got a lot going on here. We recall our previous lessons on power rules and the one I'm going to start with here is this power raised to a power. The P to the 2/7 is raised to the 28th and Q to the 3/14 is also raised to the 28th. And we recall that when we have a power raised to a power we are going to multiply those powers were going to be taking 2/7 times 28 2/7 times 28 will simplify. The seven is divided by seven. That's a 1 28 divided by seven is four. So we have two times four which is eight, we're also taking 3/14 times 28. Similar simplification here. 14 divided by 14 is 1, 28 divided by 14 is two. So three times two equals six. Rewriting our numerator with our new exponents. We've got P raised to the eighth and Q raised to the sixth all over P raised to the fifth. So now we just need to do that division. We have P to the eighth divided by P to the fifth. We recall that when we have two common basis we have two peas. And there raised two exponents. We're going to take those exponents and subtract them from each other. So we're going to take eight minus 58 minus five equals three. So that is a positive number. It's going to stick with the P. In the numerator. Soapy raised to the third times Q. Raised to the sixth. We can't write our answers with negative exponents. There to be written without negative exponents. Three and six are both positive. So this works. We look at our answer choices for P. Two the third times Q to the sixth and that matches with answer choice B. Well done, we'll catch you on the next one.

Simplify each expression. Write answers without negative exponents. Assume all vari-ables represent positive real numbers. See Examples 8 and 9. (x^1/4y^2/5)^20/x^2

Key Concepts

Exponents and Powers

Negative Exponents

Simplifying Algebraic Expressions

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