1. Holt Algebra 2 1-5 Properties of Exponents In an expression of the form a n, a is the base, n is the exponent, and the quantity a n is called a power. The exponent indicates the number of times that the base is used as a factor.

2. Holt Algebra 2 1-5 Properties of Exponents When the base includes more than one symbol, it is written in parentheses. A power includes a base and an exponent. The expression 2 3 is a power of 2. It is read “2 to the third power” or “2 cubed.” Reading Math

3. Holt Algebra 2 1-5 Properties of Exponents Write the expression in expanded form. Writing Exponential Expressions in Expanded Form The base is 5z, and the exponent is 2. 5z is a factor 2 times. (5z) 2 (5z)(5z)

4. Holt Algebra 2 1-5 Properties of Exponents Write the expression in expanded form. There are two bases: h and k + 3. h is a factor 3 times, and k + 3 is a factor 2 times. Writing Exponential Expressions in Expanded Form 3h 3 (k + 3) 2 3(h)(h)(h) (k + 3)(k + 3)

5. Holt Algebra 2 1-5 Properties of Exponents Write the expression in expanded form. There are two bases: 2x–1, and y. 2x–1 is a factor 3 times, and y is a factor 2 times. –(2x – 1) 3 y 2 –(2x – 1)(2x – 1)(2x – 1)  y  y

6. Holt Algebra 2 1-5 Properties of Exponents

7. Holt Algebra 2 1-5 Properties of Exponents Caution! Do not confuse a negative exponent with a negative expression.

8. Holt Algebra 2 1-5 Properties of Exponents Simplify the expression. Simplifying Expressions with Negative Exponents The reciprocal of.

9. Holt Algebra 2 1-5 Properties of Exponents Write the expression in expanded form. The reciprocal of. (–5) –5 5 1 5       

10. Holt Algebra 2 1-5 Properties of Exponents

11. Holt Algebra 2 1-5 Properties of Exponents Simplify the expression. Assume all variables are nonzero. Using Properties of Exponents to Simplify Expressions Product of Powers Simplify. 3z 7 (–4z 2 ) 3  (–4)  z 7  z 2 –12z 7 + 2 –12z 9

12. Holt Algebra 2 1-5 Properties of Exponents Simplify the expression. Assume all variables are nonzero. Using Properties of Exponents to Simplify Expressions Quotient of Powers Negative of Exponent Property Power of a Product (yz 3 – 5 ) 3 = (yz –2 ) 3 y 3 (z –2 ) 3 y 3 z (–2)(3)

13. Holt Algebra 2 1-5 Properties of Exponents Negative Exponent Property Power of a Power Simplify the expression. Assume all variables are nonzero. (–2a 3 b) –3

14. Holt Algebra 2 1-5 Properties of Exponents Scientific notation is a method of writing numbers by using powers of 10. In scientific notation, a number takes a form m  10 n, where 1 ≤ m <10 and n is an integer. You can use the properties of exponents to calculate with numbers expressed in scientific notation.

15. Holt Algebra 2 1-5 Properties of Exponents Simplify the expression. Write the answer in scientific notation. Simplifying Expressions Involving Scientific Notation Divide 4.5 by 1.5 and subtract exponents: –5 – 6 = –11. 3.0  10 –11

16. Holt Algebra 2 1-5 Properties of Exponents Because 22.1 > 10, move the decimal point left 1 place and add 1 to the exponent. Multiply 2.6 and 8.5 and add exponents: 4 + 7 = 11. Simplify the expression. Write the answer in scientific notation. Simplifying Expressions Involving Scientific Notation 22.1  10 11 (2.6)(8.5)  (10 4 )(10 7 ) (2.6  10 4 )(8.5  10 7 ) 2.21  10 12

17. Holt Algebra 2 1-5 Properties of Exponents Simplify the expression. Write the answer in scientific notation. Because 0.25 < 10, move the decimal point right 1 place and subtract 1 from the exponent. Divide 2.325 by 9.3 and subtract exponents: 6 – 9 = –3. 0.25  10 –3 2.5  10 –4