Simplify each expression. See Example 1.

n⁶ • n⁴ • n

Question

Simplify each expression. See Example 1.

n⁶ • n⁴ • n

Accepted Answer

Welcome back. I am so glad you're here. We're told for the following polynomial expression. Simplify, our expression is R raised to the seventh power multiplied by R raised to the fifth power multiplied by R cubed. Our answer choices are answer choice A three R raise to the 105th power answer choice B three R raise to the 15th power answer choice. Cr raise to the 15th power and answer choice. Dr raise to the 105th power. All right. So we look at our expression here and we see that we have three terms with the same base. This R raises to the seventh R raise to the fifth and R cubed all have a base of R, but they all three also have exponents. So we recall from previous lessons that when we have terms being multiplied with the same base and with exponents, we need to look at the rules for exponents. And the applicable rule here is if we have two or more terms with the same base. So let's say we had M raised to the A multiplied by M raised to the B, we say they see that they have the same base. We're going to keep that base, they still equal M, but we're going to add, they're exponents. So it's going to be M raised to the A plus B. So here with our three RS being multiplied together, we're still going to have R as our base, but we are going to be adding all of these exponents. So seven plus five plus three equals 15. So this simplifies to be R raise to the 15th power. We look at our answer choices and this matches with answer choice. C well done. We'll catch you on the next one.

Simplify each expression. See Example 1. n⁶ • n⁴ • n

Key Concepts

Exponent Rules

Multiplication of Exponents

Simplification of Algebraic Expressions

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