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

x•x³

Question

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

x•x³

Accepted Answer

Hey, everyone in this problem, we're asked to use the product rule of exponents to simplify the expression. The expression we given is P multiplied by P to the exponent 11. We're given four answer choices. Option A is P to the exponent 1/11. Option B is P to the exponent 11. Option C is one divided by P to the exponent 10. And auction D is P to the exponent 12. We're gonna start by rewriting the expression we were given P multiplied by P to the exponent 11. Now recall the product rule of exponent. If we have two things multiplied together, that have the same base, we can combine these into one term where the exponents are at it. So if we have X to the exponent N multiplied by X to the exponent and says equal to X to the exponent M plus N, OK. So we keep that same base of X. Let me add the exponents applying this to our problem. We have P OK. And this has an exponent of one. So P to the exponent one multiplied by P to the exponent 11, we can write this as P to the exponent one plus 11, we can simplify that exponent. We're just gonna add like we always do in the regular way we get that this is equal to P to the exponent 12. And so that is the simplified version of this expression. If we compare this to the answer choices, we found the simplified expression is P to the exponent 12 which corresponds with answer choice D. That's it for this one. I hope this video helped see you in the next one.

In Exercises 1–14, multiply using the product rule. x•x³

Key Concepts

Product Rule of Exponents

Exponent Notation

Simplifying Expressions

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