In Exercises 1–14, multiply using the product rule.

(5x³y⁴)(20x⁷...

Question

In Exercises 1–14, multiply using the product rule.

(5x³y⁴)(20x⁷y⁸)

Accepted Answer

Hey, everyone in this problem, we're asked to use the product rule of exponents to simplify the expression. The expression we're given, we have one term eight A to the exponent five B to the exponent eight multiplied by a second term 13 A to the exponent nine B to the exponent 11. We're given four answer choices. Option a 21 a to the exponent five nights B to the exponent 8, 11th, option B 21 A to the exponent B to the exponent 88. Option C 104 A to the exponent 14 B to the exponent in option D 104 A to the exponent 19 B to the exponent 14. We're gonna start by rewriting the expression we were given. So we have the first term eight A to the exponent five B to the exponent eight multiplied by 13 A to the exponent nine B to the exponent 11. We multiply let's start by looking at the coefficient in front. OK. So just the number term. So we have eight from the first multiplied by 13, from that second term. So we're gonna end up with eight multiplied by 13. We have a to the exponent five multiplied by a to the exponent nine. Now recall that if we have two things multiplied together with the same base, the exponents are going to add. Yeah, what do I get? Well, if we have X to the exponent M can we multiply this by X to the exponent N, this is equal to writing X that same base to the exponent M plus N. We keep the same base and we add the two exponents applying this. In our case, we're gonna have A to the exponent five plus nine. And we can apply the same rule for B, we have B to the exponent eight multiplied by B to the exponent 11. This is equivalent to writing B to the exponent 8 plus 11. OK. So we've grouped things together. Now we've grouped our coefficients, we've grouped our A terms, we've grouped our B terms and used our exponent rules. Now, we need to simplify a little bit further. So we have eight multiplied by 13. This is gonna give us 104. We have A to the exponent five plus nine. We can simplify that exponent to 14. We have A to the exponent 14 and then we have B to the exponent eight plus 11. We can simplify that exponent as well and we have B to the exponent 90. Now we have that single coefficient, a single, a term, a single B term, everything's as simplified as we can have it. And so this is the result we were looking for. If we compare this to our answer choices, we found the simplified version of the expression is 104 A to the exponent B to the exponent 19 which corresponds with answer choice. C thanks everyone for watching. I hope this video helped see you in the next one.

In Exercises 1–14, multiply using the product rule. (5x³y⁴)(20x⁷y⁸)

Key Concepts

Product Rule

Multiplying Monomials

Combining Like Terms

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