Exponents and Polynomials - XYZ Custom Plus

Multiplication with Exponents12.1oBJECtiVEsNOT FOR SALE. Copyright XYZtextbooks Last retiCkEt to suCCEssKeep these questions in mind as you read through the section. Then respond in yourown words and in complete sentences.1. Explain the difference between −​5 2 and (−5) 2 .2. How do you multiply two expressions containing exponents when they eachhave the same base?3. Explain in words how you would use the power property and the distributiveproperty for exponents to simplify (2x 3 ) 2 .4. How would you write 5,190,000 in scientific notation?During a race, a thirty-year-old marathon runner’s heart beat 145 times perminute. If he ran the marathon in 4.5 hours, his heart beat roughly 39,150 timesduring the race. In this chapter, we will learn how to write this large number inscientific notation. For instance, 39,150 can be written as 3.915 x 10 4 . But first, wemust learn to evaluate exponents and work with the properties of exponents tofurther understand their meaning in this notation.AEvaluating ExponentsRecall that an exponent is a number written just above and to the right of anothernumber, which is called the base. In the expression 5 2 , for example, the exponentis 2 and the base is 5. The expression 5 2 is read “5 to the second power” or “5squared.” The meaning of the expression is5 2 = 5 ⋅ 5 = 25In the expression 5 3 , the exponent is 3 and the base is 5. The expression 5 3 isread “5 to the third power” or “5 cubed.” The meaning of the expression is5 3 = 5 ⋅ 5 ⋅ 5 = 12512.1 Multiplication with ExponentsRixxo/Shutterstock.comABCDEuse the definition of integerexponents to evaluateexpressions containingexponents.use the product propertyfor exponents.use the power propertyfor exponents.use the distributive property forexponents.Write numbers in scientificnotation and expanded form.753