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

Question

Simplify each expression. Write answers without negative exponents. Assume all vari-ables represent nonzero real numbers. See Examples 5 and 6. (3pq)q^2/6p^2q^4

Accepted Answer

Hey everyone here we are asked to simplify the given expression where we have the quantity of two times C. Times D. Times D. To the power of five. And this is all divided by 12 times C. To the power of six times D. To the power of 15. So now to simplify this given expression we need to utilize the rules of exponents. So the first rule of exponents that we need to recall is the product rule which tells us that A. To the power of M times A. To the power of N is equivalent to A. To the power of M plus N. So now we can use this rule to simplify our numerator. So we have two times C. Times D. And now our like bass is D. So we can add the enumerators. So we have D raised to the power of one plus five. And now this is all divided by our denominator which remains unchanged for now. And it is 12 times six. Sorry, 12 times C. To the power of six times D. To the power of 15. So now we can just simplify the exponents in our numerator. So our expression becomes two times C. Times D. To the power of six. All divided by 12 times C. To the power of six times D. To the power of 15. So now from here we just need to recall our next rule of exponents which is the quotient rule and the quotient rule tells us that A. To the power of M divided by A. To the power of N. Is equivalent to A. To the power of m minus N. So now we can use this rule this quotient rule to divide our expression here. So we have two divided by 12 times C. To the power of one. Because that is the power in the numerator for C minus six. Since it is the power in the denominator for C. And this term is multiplied by D. Which is raised to the power of six minus 15. And so now we just need to simplify our expression here and we see two divided by 12 simplifies to 16. And then this is multiplied by C. Which is raised to the power of negative five and then D. Is simplified to negative nine. And so now now our last step here is to recall the rule for a negative exponents which tells us that a. To the power of negative end is equivalent to one divided by A. To the power of N. So now again we can use this negative exponents rule to rewrite our expression. We see that we have both variables raised to a negative power so they will both go into the denominator. So our expression becomes one divided by the quantity of six times C. To the power of positive five times D. To the power of positive nine. And with this we have fully simplified our original expression and so we are left with answer choice. B. Thanks for watching. I hope you found this video helpful, and I'll see you again next time.

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Simplify each expression. Write answers without negative exponents. Assume all vari-ables represent nonzero real numbers. See Examples 5 and 6. (3pq)q^2/6p^2q^4

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