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Exponents in Mathematics

Learn the properties and rules of exponents, including multiplying powers with the same base, power of a power, and power of a product. Practice examples for better comprehension. Understand the division properties and finding quotients of powers.

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Exponents in Mathematics

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  1. PROPERTIES of EXPONENTS

  2. Location of Exponent • An exponent is a little number high and to the right of a regular or base number. Exponent 3 4 Base

  3. Definition of Exponent • An exponent tells how many times a number is multiplied by itself. Exponent 3 4 Base

  4. What an Exponent Represents • An exponent tells how many times a number is multiplied by itself. 4 = 3 x 3 x 3 x 3 3

  5. How to read an Exponent • This exponent is read three to the fourth power. Exponent 3 4 Base

  6. Properties

  7. MULTIPLYING POWERS WITH THE SAME BASE Numbers Algebra Words To multiply powers with the same base, keep the base and add the exponents. bm • bn = bm + n 35 • 38 = 35 + 8 = 313

  8. 1. 66 •63 Alone! Together! 1. 42 •44 2. x2 •x3 2. n5 •n7 3. x5 • y2 3. 25 • 2 4.412• 417 4.244• 244

  9. Multiplying Power of a Power Numbers Algebra Words To multiply power of a power, keep the base and multiply the exponents. (pr)s = pr •s NOTE: Multiply the exponents, not add them!

  10. Alone! Together! 1. (y4)2 1. (x2)3 2. (3)6 3. (2⁶)² 4. (6²)³ 2. (55)2 3. (3²)⁴ 4. (4)²

  11. Power of a Product (a · b)ᴹ = aᴹ · bᴹ To raise a product to a power, raise each factor to the power Example (5 · 7)² = 5² · 7² (4x)³ = 4³ · x³

  12. Alone! Together! 1. (3y)2 1. (7x)3 2. (3 · 2)6 3. (2⁶x)² 4. 4³ · 2³ 2. (5 · 3)2 3. (3²x³)⁴ 4. 3² · 5²

  13. 6.) (3a)3 •(2p)2 7.) w3• (3w)4 8.) 7² · 3² 9.) (3² x³)⁴ 10.)(x2y3)2 1.) b2• b7 2.) (p3)4 3.) (a2)3• a3 4.) x2• (xy)2 5.) (4m)2 • m3 Pair- Practice!

  14. Ex: Multiplying Polynomials: In multiplying polynomials, you have to multiply the coefficients and add up the exponents of the variables with the same base.

  15. Please simplify the following equations: How?: Answer:

  16. Division Properties of Exponents

  17. Finding Quotients of Powers Simplify Alone Together A. A. B. B. C. C. D. D.

  18. Finding Positive Powers of Quotient Simplify. Alone Together A. A. B. B. C. C.

  19. Remember that What if x is a fraction?

  20. Finding Negative Powers of Quotients Simplify. Alone Together A. A. B. B. C. C.

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