Find each product. Assume all variables represent positive real n...

Question

Find each product. Assume all variables represent positive real numbers. -4k(k^7/3-6k^1/3)

Accepted Answer

Welcome back. I am so glad you're here. We are Given this expression eight p times p raised to the 13 5th minus three P. Raised to the 2/5 and we are asked to determine the product or in other words we're going to distribute this eight P. To the two terms inside the parentheses. We're going to multiply. So we could rewrite this as eight P times P. To the 13 5th minus eight p. Times three P. Two. The 2/5. And now we just need to do that multiplication. Well we see that we have these P. S. Being multiplied and the second P has an exponent. We recall from previous lessons that when we are multiplying variables with exponents we are going to add their exponents together. But what's the exponents for that? P. By itself. Well the exponents for P when none is written is one. So for the first one we're taking one plus 5th and for the second one we're taking one plus 2/5. Well to add fractions we need a common denominator. What would our common denominator be? It's five. So we need to take one and multiply that by 5/5. So this is 5/5 plus 5th for the first one and likewise the common denominator will be five on this side. So that's 5/5 plus 2/5. Now that we've got a common denominator. We can add the new Raiders. Five plus 13 is 18. So this new exponent will be 18, 5th and five plus two is seven. So this new exponent will be 7/5. So let's write that down. We've got eight P raised to the 18 5th. So for the first one minus and on the second one we do have the coefficients eight times three. So this will be minus 24 P. And we said the new exponent was raised to the 7/5. So we look at our answer choices, looking for eight P. To the 18 5th minus 24 P. To the 7/5 that matches with answer choice D. Well done, we'll catch you on the next one.

Find each product. Assume all variables represent positive real numbers. -4k(k^7/3-6k^1/3)

Key Concepts

Factoring

Exponents and Powers

Distributive Property

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