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Laws of Exponents

Laws of Exponents. Zero Rule. Any non-zero number raised to the zero power equals one X 0 = 1 Examples: 2 0 =1 99 0 = 1. Rule of One. Any number raised to the power of one equals itself. x 1 =x Examples: 17 1 = 17 99 1 = 99.

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Laws of Exponents

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  1. Laws of Exponents

  2. Zero Rule Any non-zero number raised to the zero power equals one X0 = 1 Examples: 20=1 990= 1

  3. Rule of One Any number raised to the power of one equals itself. x1=x Examples: 171 = 17 991 = 99 Well this one is easy!

  4. Product Rule When multiplying two powers with the samebase, keep the base and add the exponents. xa • xb = xa+b Examples : 42 • 43 = 45 95• 98 = 913 Now here’s a harder one! (x2y4)(x5y6) = x7y10

  5. Quotient Rule When dividing two powers with the same base, keep the base and subtract the exponents. xa÷ xb = xa-b Examples : 75 ÷ 73 = 72 28÷ 22 = 26 Remember that division can also be written vertically: Now here’s a harder one!

  6. But what happens if you add or subtract the exponents and you get a negative number ? First of all, there is no crying in math! Second, we have a law for that too! It’s called the Negative Rule! Let me tell you all about it…

  7. Negative Rule Any non-zero number raised to a negative power equals its reciprocal raised to the opposite positive power. WHAT!!

  8. …Negative Rule If we apply the negative rule (Any non-zero number raised to a negative power equals its reciprocal raised to the opposite positive power) then,

  9. Power Rule When raising a power to a power, keep the base and multiply the exponents. (xa)b = xa•b Let me jot this down. Oh yes, I got it now! Examples: (24)3 = 212 (x3)5 = x15

  10. Product to a Power Rule A product raised to a power is equal to each base in the product raised to that exponent. (x• y)2 = x2y2 Examples: (7• 3)2 = 72 •32 = 49 • 9 =441 Here’s one where the variables have exponents Here’s one where the product is raised to a negative power! Tricky, trickier, trickiest – But I think I got it!

  11. (x3y2)5 = x15y10 • (2x2yz-3)-4 = 2-4x-8 y-4 z12 =

  12. Quotient to a Power Rule A quotient raised to a power is equal to each base in the numerator and denominator raised to that exponent. Examples: …and this is the last law!

  13. Example 1- • Simplify

  14. Example 2- Select a strategy to evaluate an expression with 2 variables. Correct Strategy: Simplify first. Then substitute in the value of variables And simplify again

  15. KEY CONCEPTS • Exponent laws are only if the BASES ARE SAME. • It is efficient to SIMPLIFY an algebraic expression before substituting the values of variables. • DONOT CHANGE fractions to decimals to evaluate. [rounding will create errors in answers]

  16. Homework • Page 2 and 3 of your workbook – “Exponents –Multiplying and Dividing”

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