1-5 Properties of Exponents - Belton ISD / Home

1 Holt Algebra 2 1-5 Properties of Exponents Zero exponent Property: Any nonzero value raised to the zero power equals 1. 1000 = 1 a0 = 1 Negative exponent Property: Any nonzero base raised to a negative exponent is equal to the reciprocal of the based raised to the positive exponent . 7 2=172=172 =1 =1 Holt Algebra 2 1-5 Properties of Exponents Simplify the expression. Example 2A: Simplifying Expressions with Negative Exponents The reciprocal of . 3 2 Holt Algebra 2 1-5 Properties of Exponents Simplify the expression. Example 2B: Simplifying Expressions with Negative Exponents The reciprocal of . Holt Algebra 2 1-5 Properties of Exponents Check It Out! Example 2a Simplify the expression.

2 The reciprocal of x-3 is 1 3. 3 2 1 3 1 2 1 3 2 Holt Algebra 2 1-5 Properties of Exponents Product of Powers Property: To multiply powers with the same base, add the Exponents . 43 42 = 43+2 = 45 am + an = am+n Quotient of Powers Property: To divide powers with the same base, subtract the Exponents . 3732=37 2=35 = Holt Algebra 2 1-5 Properties of Exponents Power to a Power Property: To raise one power to another power, multiply the Exponents . (43)2= 43 2 = 46 (am)n= am n Power of Product Property: To find the power of a product, apply the Exponents to each factor. (3 4)2= 32 42 (ab)n= an bn Holt Algebra 2 1-5 Properties of Exponents Power of a Quotient Property: To find the power of a quotient, apply the exponent to the numerator and denominator.

3 352=3252 = Holt Algebra 2 1-5 Properties of Exponents Simplify the expression. Assume all variables are nonzero. Example 3A: Using Properties of Exponents to Simplify Expressions Product of Powers Simplify. 3z7( 4z2) 3 ( 4) z7 z2 12z7 + 2 12z9 Holt Algebra 2 1-5 Properties of Exponents Simplify the expression. Assume all variables are nonzero. Example 3B: Using Properties of Exponents to Simplify Expressions Quotient of Powers Negative of exponent Property Power of a Product Power of a Product (yz3 5)3 = (yz 2)3 y3(z 2)3 y3z( 2)(3) Holt Algebra 2 1-5 Properties of Exponents Check It Out! Example 3a Simplify the expression. Assume all variables are nonzero. Power of a Power Power of a Product (5x6)3 53(x6)3 125x(6)(3) 125x18 Holt Algebra 2 1-5 Properties of Exponents Negative exponent Property Power of a Power Check It Out!

4 Example 3b Simplify the expression. Assume all variables are nonzero. ( 2a3b) 3 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 10n, where 1 m <10 and n is an integer. Divide by and subtract Exponents : 5 6 = 11. 10 11 Ex) Holt Algebra 2 1-5 Properties of Exponents Because > 10, move the decimal point left 1 place and add 1 to the exponent . Multiply and and add Exponents : 4 + 7 = 11. Simplify the expression. Write the answer in scientific notation. Example 4B: Simplifying Expressions Involving Scientific Notation 1011 ( )( ) (104)(107) ( 104)( 107) 1012 Holt Algebra 2 1-5 Properties of Exponents Check It Out!

5 Example 4a Simplify the expression. Write the answer in scientific notation. Because < 10, move the decimal point right 1 place and subtract 1 from the exponent . Divide by and subtract Exponents : 6 9 = 3. 10 3 10 4 Holt Algebra 2 1-5 Properties of Exponents HW pg. 39 # s 30-38, 42, 45-50 Holt Algebra 2 1-5 Properties of Exponents HW pg. 38 # s 6-20, 43, 44