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# Expanding Exponent Products

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### Expanding Exponent Products

1. 1. Image Source: http://upload.wikimedia.org
2. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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).