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^2/3)^2/(x^2)^7/3

Accepted Answer

Welcome back. I am so glad you're here. We are given this expression we have a two the 2/5 C raised to the fourth in the numerator that's divided by a to the third raised to the 4/ and we are to simplify. So the first rule of exponents that I'd like us to recall is when we have a power raised to a power which is occurring in both the numerator and the denominator. Here we are going to multiply those exponents by each other. So in the numerator will have 2/5 times 4 2/5 times four equals 8/5. In the denominator we have three times 4/ three times 4/5 equals 12 5th. So rewriting our numerator with its new exponent will be a two. The 8/5. And rewriting our denominator with the new exponent will be a to the 5th. Now the next rule of exponents that I'd like us to recall is that when we are dividing variables with the same base they both have a base of A. And they have exponents we're going to subtract those exponents from each other. So we're going to take 8/5 minus 5th. We have a common denominator. So we can just subtract up in the numerator eight minus 12 equals negative. We have negative 4/5. We can rewrite our variable a with its new exponent negative. 4/5. Now we can't write our answer with a negative exponent we need to write it without negative exponents. So we recall that when we've got a negative exponent that negative is telling us that our variable is on the wrong side of the division line. That this a needs to get to the denominator and when it does that negative in the exponent will disappear. So we're going to put a one in its place for the numerator and then we'll bring a to the now positive for fifths to the denominator. And now we've written it with a positive exponents. We look at our answer choices for one over a to the 4/ and that matches with answer choice. A Well done, we'll catch you on the next one.

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Simplify each expression. Write answers without negative exponents. Assume all vari-ables represent positive real numbers. See Examples 8 and 9. (x^2/3)^2/(x^2)^7/3