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. (5a^-1)^4(a^2)^-3

Accepted Answer

Hey everyone here we are asked to simplify the given expression where we have the quantity of three times C. To the power of negative four raised to the power of three times the quantity of C. To the power of four raised to the power of six. So to simplify our expression, we need to utilize the rules of exponents. So the first rule of exponents that we need to recall is the power to a power rule, which tells us that the quantity of A. To the power of M raised to the power of N is equivalent to A. To the power of M times N. So with this rule in mind we can go ahead and rewrite our original expression. So beginning with our first term here which is raised to the power of three. We can rewrite it as the quantity of three to the power of one times three. And this is multiplied by C. Which is raised to the power of negative four times three. So now we can move on to our second term in our original expression where we have the quantity of C. To the power of four raised to the power of six. And now we can rewrite it as the quantity of C. To the power of four times six. And so now from here We just need to simplify our exponents here in our expression. So doing this, we get the quantity of three to the power of three times c. To the power of negative 12 times the quantity of C to the power of 24. And so now we need to recall our next rule of rule for exponents and this is going to be the product rule, while the product rule states 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 again we need to use this rule to rewrite our expression that we have found so far. So doing this, we have our coefficient here which is just three to the power of three, but now we can simplify our C. Variable. So C. Is now raised to the power of negative 12 plus 24 according to our product rule. So now we can just again simplify our exponents here. So we have three to the power of three times C. To the power of 12. And now our last simplification here just has to do with our coefficient here. Well three cubed is just 27. So our final answer simplified becomes 27 times C. To the power of 12. And this leaves us with answer choice B. Thanks for watching. I hope you found this video helpful and I'll see you again next time

Simplify each expression. Write answers without negative exponents. Assume all vari-ables represent nonzero real numbers. See Examples 5 and 6. (5a^-1)^4(a^2)^-3

Key Concepts

Exponents and Power Rules

Negative Exponents

Combining Like Terms

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