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8th Grade Slides. Exponents. Exponents. Key Skill: Calculate values of expressions with positive and negative exponents. Quick Review. Exponent. Base. Exponent Review. Repeated multiplication:. Exponent Review. Any number to the first power is?. Exponent Review.

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## 8th Grade Slides

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**8th Grade Slides**Exponents**Exponents**• Key Skill: Calculate values of expressions with positive and negative exponents.**Quick Review**Exponent Base**Exponent Review**• Repeated multiplication:**Exponent Review**• Any number to the first power is?**Exponent Review**• Any number to the first power is itself • So • And**Exponent Review**• Any non-zero number to the power of 0 is?**Exponent Review**• Any non-zero number to the power of 0 is 1. • So, • and (assuming x does not = 0),**Question**• What is**Question**• What is • Is it the same as**Odd and Even Exponents**• Will a negative number raised to a power always be positive?**Odd and Even Exponents**• How do we know whether a negative number raised to a particular power will be positive or negative?**Odd and Even Exponents**• How do we know whether a negative number raised to a particular power will be positive or negative? Negative base with an odd exponent results in a NEGATIVE answer Negative base with an even exponent results in a POSITIVE answer**Decimals and Fractions**• Is this the same as**Decimals and Fractions**• Is this the same as No!**Negative Exponents**• Look at this progression of numbers: 33 = 32 = 31 = 30 = 3-1 = 3-2 = 3-3 =**Negative Exponents**• Look at this progression of numbers: 33 = 27 32 = 9 31 = 3 30 = 1 3-1 = 1/3 3-2 = 1/9 3-3 = 1/27**Negative Exponents**• Rule:**Negative Exponents**• The reverse is also true:**Negative Exponents**• We generally do NOT want negative exponents in our answer (unless we are using Scientific Notation). • We move bases with negative exponents to the denominator where they will turn positive. • If a negative exponent is found in a denominator, we move it to the numerator.**Method**Step 1: Take the RECIPROCAL of the base. What does RECIPROCAL MEAN? Step 2: The exponent moves with the base, but the negative sign in the exponent disappears.**Exception**• Numbers generally get LARGER when we square them. What kind of numbers get SMALLER when we square them?**Exception**• Numbers generally get LARGER when we square them. What kind of numbers get SMALLER when we square them? • Numbers between 0 and 1 (fractions and decimals)**Classwork**• Pages**Exponent Laws**• Key Skill: Apply the Laws of Exponents to simplify expressions.**Exponents**• Reminders: • Anything raised to the power of 1 is itself. • Any non-zero number raised to the power of 0 is 1. • When we see we use PEMDAS to determine what to do first. • In this case, raise ‘x’ to the 3rd power, THEN multiply by 4**PEMDAS**Parentheses ( ) Exponents 3 Multiplication x, Division ÷ Addition + Subtraction __**Please**Excuse My Dear Aunt Sally • Parentheses ( ) • Exponents 3 • Multiplication x, • Division ÷ • Addition + • Subtraction __**Product Law of Exponents**• How would we multiply:**Product Law of Exponents**• How would we multiply: • We could rewrite it as: (4 x 4 x 4) x (4 x 4)**Product Law of Exponents**• How would we multiply: • We could rewrite it as: (4 x 4 x 4) x (4 x 4) • Or with an exponent: • Note that we did NOT multiply the exponents, we ADDED them!**Another Example**• How would we multiply:**Another Example**• How would we multiply: • We would rewrite the equation as: • Or more simply as: 32 • Again, we ADDED the exponents**Example with a variable**• What is:**Example with a variable**• What is: • Rewrite as: • Or more simply as:**Contra-Example**• Does the Product Law of Exponents apply here?**Contra-Example**• Does the Product Law of Exponents apply here? • No! We do NOT have a common base or a common exponent.**Product Law of Exponents**• What about:**Product Law of Exponents**• What about: • Does it matter what order we write the factors?**Product Law of Exponents**• What about: • Does it matter what order we write the factors? • How about:**Product Law of Exponents**• What about: • Does it matter what order we write the factors? • How about:**The Other Product Law**• How would we work with: • What’s different/what’s the same?**The Other Product Law**• How would we work with: • We can rewrite as: (4 x 4) x (3 x 3) • Or as (4 x 3) x (4 x 3) because order doesn’t matter when we multiply**The Other Product Law**• How would we work with: • We can rewrite as: (4 x 4) x (3 x 3) • Or as (4 x 3) x (4 x 3) because order doesn’t matter when we multiply • Now we can rewrite as**The Other Product Law**• How would we work with: • What’s different/what’s the same?

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