Expanding Exponent Products

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  • 1. Image Source: http://upload.wikimedia.org
  • 2. This “Multiply Rule” only works if there is one Base in the BracketsThe Power of Power Rulelets us simply multiply thePower values to get theexpanded form of this item.(23) 2= 23 x 2= 26We need to use a different rule if there are 2 or more Bases in brackets(2a3)2is not 2a3 x 2= 2a6
  • 3. Eg. The 2 and the a BOTH need to be squared.(2a)2= 2a x 2a = 2x2 x axa = 4a2Using the Expanding Products Rule we do the following :(2a)2= 22x a2= 4 x a2= 4a2
  • 4. Eg. The 2 and the a BOTH need to raised to 2.The Power outside the brackets needs to be applied to all BasesInside the brackets. (Like the Distributive Law, but for Exponents).(2a)2= 22x a2= 4 x a2= 4a2
  • 5. Eg. The 2 and the a3BOTH need to be squared.(2a3)2= 2a3x 2a3= 2x2xa3xa3= 4a6Using the Expanding Products Rule we do the following :(2a3)2= 22x a3 x 2= 4 x a6= 4a6
  • 6. Simplify the expression (2 x 5)4We apply the Outside Power to both items:(2 x 5)4= 2 4x 5 4= 24x 54
  • 7. Simplify the expression (23x 52)4We apply the Outside Power to both items:(23x52)4= 23 x 4x 52 x 4= 212x 58= 212x 58
  • 8. Simplify the expression (m3k2)4We apply the Outside Power to both items:(m3k2)4= m3 x 4x k2 x 4= m12x k8= m12k8
  • 9. Simplify the expression (5d4)2We apply the Outside Power to both items:(5d4)2= 5 2x d4 x 2= 25 x d8= 25d8
  • 10. Simplify the expression (a2m3k2)5We apply the Outside Power to all 3 items:(a2m3k2)5= a2 x 5x m3 x 5x k2 x 5= a10x m15x k10= a10m15k10
  • 11. We can also use the Expanding Products Rule BACKWARDS tosimplify expressions like the following :2 4x 5 4= (2 x 5)4= 104m 3x t 3= (m x t)3= (mt)3
  • 12. 3 2x 2 2= (3 x 2)2= (6)2= 622 5x k 5= (2 x k)5= (2k)5p 3x q 3= (p x q)3= (pq)3For Expanding Products Rule BACKWARDS, we have two differentbases, BUT THEY MUST BOTH BE RAISED TO THE SAME POWER.
  • 13. We also use the Products Rule Backwards to combine same Powers.The Power outside the brackets needs to be applied to all BasesInside the brackets. (Like the Distributive Law, but for Exponents).
  • 14. http://passyworldofmathematics.comVisit our Site for Free Mathematics PowerPoints