Presentation on theme: "Warm-up: Check your homework!"— Presentation transcript:
1 Warm-up: Check your homework! Lesson 7.3: Define and Use Zero and Negative Exponents Essential Question: How do you evaluate exponential expressions involving zero and negative exponents?Warm-up: Check your homework!Common CoreCC.9-12.A.SSE.3cUse the properties of exponents to transform expressions for exponential functions.
4 Definition of Zero and Negative Exponents Wordsa to the zero power is 1.𝒂 −𝒏 is the reciprocal of 𝒂 𝒏.𝒂 𝒏 is the reciprocal of 𝒂 −𝒏 .Algebra Example
5 Use definition of zero and negative exponents EXAMPLE 1Use definition of zero and negative exponents132=a. 3– 2Definition of negative exponents19=Evaluate exponent.b. (–7)0= 1Definition of zero exponent
6 Use definition of zero and negative exponents EXAMPLE 1Use definition of zero and negative exponents5–21c.=152Definition of negative exponents125=Evaluate exponent.= 25Simplify by multiplying numeratorand denominator by 25.10 5(Undefined)=d – 5a – n is defined only for a nonzeronumber a.
7 GUIDED PRACTICEfor Example 1Evaluate the expression.231.123.–3=1= 82. (–8) – 2164=4. (–1 )0= 1
8 Properties of Exponents Let a and b be real numbers, and let m and n be integers.Product of powers propertyPower of a power propertyPower of a product propertyQuotient of powers propertyPower of a quotient property
9 Evaluate exponential expressions EXAMPLE 2Evaluate exponential expressionsa. 6–= 6– 4 + 4Product of a power property= 60Add exponents.= 1Definition of zero exponent
10 Evaluate exponential expressions EXAMPLE 2Evaluate exponential expressionsb. (4– 2)2= 4– 2 ∙ 2Power of a power property= 4– 4Multiply exponents.14=Definition of negative exponents1256=Evaluate power.c.13– 4= 34Definition of negative exponents= 81Evaluate power.
11 Evaluate exponential expressions EXAMPLE 2Evaluate exponential expressionsd.5– 152= 5– 1 – 2Quotient of powers property= 5– 3Subtract exponents.153=Definition of negative exponents1125=Evaluate power.
13 Use properties of exponents EXAMPLE 3Use properties of exponentsSimplify the expression. Write your answer using only positive exponents.a. (2xy–5)3= 23 x3 (y–5)3Power of a product property= 8 x3 y–15Power of a power property=y158x3Definition of negative exponents
14 Use properties of exponents EXAMPLE 3Use properties of exponents(2x)–2y5–4x2y2b.y5(2x)2(–4x2y2)=Definition of negative exponentsy5(4x)2(–4x2y2)=Power of a product propertyy5–16x4y2=Product of powers propertyy316x4–=Quotient of powers property
15 EXAMPLE 4Standardized Test PracticeThe order of magnitude of the mass of a polyphemus moth larva when it hatches is 10-3 gram. During the first 56 days of its life, the moth larva can eat about 105 times its own mass in food. About how many grams of food can the moth larva eat during its first 56 days?A10–15 gramBgramC100 gramsD10,000,000 grams
16 EXAMPLE 4Standardized Test PracticeSOLUTIONTo find the amount of food the moth larva can eat in the first 56 days of its life, multiply its original mass, 10– 3, by 105.–3= (–3)= 102= 100The moth larva can eat about 100 grams of food in the first 56 days of its life.ANSWERThe correct answer is C.ABCD
17 GUIDED PRACTICEfor Examples 3 and 49x3y3xy – 39. Simplify the expression Write your answerusing only positive exponents.13x2y4ANSWER10. SCIENCE The order of magnitude of the mass of a proton is 104 times greater than the order of magnitude of the mass of an electron, which is 10–27 gram. Find the order of magnitude of the mass of a proton.ANSWER10 –23 g