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The Power Rules

The Power Rules . x a. ( x a ) b. x a • b. =. y b. =. ( x a y b ) c. x a • c. y b • c. x a • c. =. y b • c. ( ). c. 12. Simplify. a . (a 4 ). 3. a 4 • 3. a 12. (a 4 )( a 4 )( a 4 ). Can write it three times. . Add 4 three times or multiply the exponents. 12. Simplify.

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The Power Rules

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  1. The Power Rules xa (xa)b xa •b = yb = (xayb)c xa •c yb•c xa • c = yb• c ( ) c

  2. 12. Simplify. a. (a4) 3 a4 • 3 a12 (a4)(a4)(a4) Can write it three times. Add 4 three timesor multiply the exponents.

  3. 12. Simplify. b. (105)2 105• 2 1010 Multiply the exponents.

  4. 12. Simplify. c. (-1)15 -1 Multiply -1 an odd number (15) of times.

  5. 13. Simplify. a. (3xy)3 (3)3 x1 • 3 y1 • 3 27 x3 y3 Keep 3 in the parentheses. Multiply the exponents. Evaluate each.

  6. 13. Simplify. b. (yz)37 y1 • 37 z1 • 37 y37 z37 Multiply the exponents. Evaluate each.

  7. 13. Simplify. c. (-3x3)2 (-3)2 x3• 2 9 x6 Keep -3 in the parentheses. Multiply the exponents. Evaluate each.

  8. 14. Simplify. x a. ( )3 5 x3 (5)3 x3 125 Multiply the exponents. Keep 5 in the parentheses. Evaluate.

  9. 14. Simplify. b. ( ) 4 a 2 a ) b ( 6 a2 16 a6 b6 16 a4 b6 Evaluate. Multiply exponents. Use quotient rule and subtract exponents.

  10. 15. Simplify. -2 x3 y0 z ( )5 x z2 4 -1 x2 ( ) 5 z 2 - x10 z5 32 Work inside parentheses. Simplify and use quotient rules. Use power rule and evaluate.

  11. The Power Rules xa (xa)b xa •b = yb = (xayb)c xa •c yb•c xa • c = yb• c ( ) c

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