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Chapter 4 Notes 4-2 Exponents Parts of an Exponent the exponent tells HOW MANY times Example the base tells WHAT number 3² means 3 x 3 = 9 −2 • a • a • a • b = −2a³b be careful of negatives (−2 )² = (−2 )(−2 ) = 4 but − 2 ² = − ( 2 • 2 ) = −4 ________________________________________________________________________________ Notes 4-7 Multiplying Exponents To multiply exponents with the same base, write the base and add the exponents. To multiply exponents with different bases, multiply the base and simplify the exponents. Taking a Power TO A POWER! This means (a²) 4 times (a²)(a²)(a²)(a²) means a• a• a• a• a• a• a• a multiply the exponents 2 x 4 = 8 =a _______________________________________________________________________________ Notes 4-8 Dividing Exponents To divide exponents with the same base, write the base and subtract the exponents. You can also end up with only a denominator. This can be written with a negative exponent Anything to the (0) exponent = 1 (xy) or on the bottom of a fraction. 2³ = 8 Follow the pattern. Each answer is cut in half. 2² = 4 2¹ = 2 2° = 1 2 =½ 2 =¼ _______________________________________________________________________________ Notes 5-9 Powers of products and Quotients To Raise a PRODUCT to a power - raise each factor to the power. (5 · 3)³ = 5³ · 3³ = 125 · 27 = 3375 To Raise a QUOTIENT to a power - raise both parts to the power. _______________________________________________________________________________ Scientific Notation always has this form Notes 4-9 One digit, a decimal, the rest of the number, X 10 to an exponent For the exponent, count the spaces the decimal must move to get to decimal to its right spot. examples 6 2,000,000 = 2 X10 BIG numbers have a POSITIVE exponent. -5 0.00004 = 4 X10 Little numbers have a NEGATIVE exponent. STANDARD FORM is just a REGULAR NUMBER.