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. (z^1/3z^-2/3z^1/6)/(z^-1/6)^3

Accepted Answer

Welcome back. I am so glad you're here. We are Given this expression in the numerator we have C. Two. The 1/5 times C. To the 7/10 times C. To the negative 2/5 all over C. To the negative 1/5 raised to the fourth. And we are to simplify this writing our answer without negative exponents. We've got a lot we could do here in a lot of different places we could start. So if you didn't solve it the same way that I did that's okay. Where I'm going to start is in the denominator we have a power raised to a power. We recall from our previous lessons on power rules that when we have a power raised to a power we're going to multiply those exponents. So our numerator or excuse me our denominator is going to be C. Raised to the negative 1/5 times four and negative 1/5 times four equals negative 4/5. So in our denominator we've got C raised to the negative 4/5 and in the numerator still see to the 1/5 times C. To the 7/10 times C. To the negative 2/5. Now what I'd like to do next is take a look at these variables that have negative exponents. We know that negative exponents tell us that they're on the wrong side of this division line that the C. With the negative 4/5 in the denominator has to go up to the numerator and the sea with the negative 2/5 in the numerator has to go down to the denominator. So I'm going to rewrite it with those in their proper positions and then the negative will disappear so we'll still have sea to the 1/5 times C. To the 7/10. And now we're bringing up C. To the now positive 4/5 into the numerator and bringing down the sea to the now positive 2/ into the denominator. Okay now there's no negative exponents. And the next thing that I'm going to do is we see in our numerator we have three CS that are being multiplied. And we know from previous lessons that when we are multiplying variables with exponents we are going to add those exponents together. So we've got 1/5 plus 7/10 plus 4/5. And we need a common denominator here which is going to be 10. So we'll multiply 4/5 times 2/2 will multiply 1/5 times 2/2. So now we'll have 2/10 plus 7/10 plus 8/10. Now we have a common denominator so we can add our numerator. I'm adding two plus eight because that's 10 plus another seven. So we have 17 10th is in our numerator. So we have C. Raised to the 17 10th over C. Raised to the 2/5. So okay now we recall that when we have two variables the same base, they're both C. And they're being divided. We are going to take their exponents and we're going to subtract them. So we are going to take 17 10th minus 2/5 and again we need a common denominator of 10. So we're going to multiply 2/5 times 2/2. So this would read 17/ -4/10 and 17 -4 is 13. So we've got 13/10 is our new exponents. So our answer is is C. Raised to the 13 10th. It has to be written without negative exponents and yes 13 10th is a positive exponent. So we are done. We look at our answer choices and this matches with answer choice. D. 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. (z^1/3z^-2/3z^1/6)/(z^-1/6)^3