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Rules of Exponents and Examples

Learn the rules of exponents and how to apply them in multiplication, division, and raising powers to powers. Explore examples to understand the concepts better.

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Rules of Exponents and Examples

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  1. 52 Exponent Base 52 · 53 = 55 If the numerical bases are the same, keep the base and add the exponents.

  2. If the bases are different, multiply the bases. If the base does not have an exponent, the exponent is one.

  3. Rules of Exponents • When multiplying bases, add exponents. • When dividing bases, subtract exponents. • When a raising a power to a power, multiply the exponents.

  4. Examples: • 3x2 · 4x8 3·4·x·x · x·x·x·x·x·x·x·x 12x10 • -2x3y2 · 8x4y3 -16x7y5

  5. 3. 7a3b2 · 4a2b4 28a5b6 4. -3bc3 · 5b3c2 -15b4c5 5. X5 x3 x·x·x·x·x x·x·x x2

  6. 23·34·45 22·32·44 2·32·4 72 45·57·69 43·55·67 42·52·62 14,400 8. 8x5y6 4x3y4 2x2y2 15a7b9 3a3b6 5a4b3 • y6 y3 y3 • a8b6 a5b5 a3b

  7. 93·84·73 92·82·72 9·82·7 4032

  8. Practice 4a4b6 · 3a2b3 2. 5x8y3· 3xy4 3. b9c4 b6c2 4. 10x5y8 2x4y6 25 ·36·45 23 ·33·44

  9. 6. (3a2)3 • (b3)4 • (4x4)5 • (5c3d3)3 • (8r5t6)3

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