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

b⁴•b⁷

Question

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

b⁴•b⁷

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 is M to the exponent multiplied by M to the exponent three, we have four answer choices. Option am to the exponent 16. Option B M to the exponent 10, option C to the exponent 13/ and option D M to the exponent 39, we're gonna start by rewriting the expression we were given M to the exponent 13 multiplied by M to the exponent three. Now we're called the product rule of exponents. If we have two things multiplied together with the same base, we can write this as one term where the exponent is the addition of the original exponents. What do I mean? Well, if we have X to the exponent, A multiplied by X to the exponent B, we can write this as X to the exponent A plus B. OK. So we multiplied two things with the same base of X together, we write them as a single term with that base of X and the original exponents A and B get added together in that new exponent. If we apply this to our problem. We can write M to the exponent 13 multiplied by M to the exponent three as M to the exponent plus three. Can we keep that same base of M? The exponents are added together? Now, we can simplify that exponent by adding and this is equal to M to the exponent 16. There's no more simplifying we can do. So this is the result we were looking for. If we compare this with our answer choices, we found that the simplified version of our expression is equal to M to the exponent 16 which corresponds with answer choice A. That's it for this video. Thanks everyone for watching. I hope this helped.

In Exercises 1–14, multiply using the product rule. b⁴•b⁷

Key Concepts

Product Rule of Exponents

Base of an Exponent

Simplifying Exponential Expressions

Watch next