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# Expanding Exponent Quotients

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• 1. Image Source: http://www.philipvaughan.net
• 2. 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
• 3. Eg. The a and the b BOTH need to be cubed.2 32 x 2 x 2 233 3 x 3 x 3 33==a 3a x a x a a3b b x b x b b3==
• 4. Eg. The a and the b BOTH need to be Powered.The Expanding Quotients Rule involvesapplying the Power Outside of thebrackets, onto every item that is insidethe brackets.
• 5. 5 45 4543 3 34Simplify the expression (5 / 3)4We apply the Outside Power to both items:==
• 6. m 6m 6m6k k k6Simplify the expression (m / k)6We apply the Outside Power to both items:==
• 7. 2h 52h 525xh525h5c4c4c4x5c20Simplify the expression ( 2h / c4) 5We apply the Outside Power to all three items:== =For the 2h, the 2 & h BOTH need to be Powered.
• 8. ab2 3ab2 3a3b2x3a3b6c c c3c3Simplify the expression ( ab2/ c ) 3We apply the Outside Power to three items:== =For the ab2, the a & b2BOTH need to be Cubed.
• 9. Eg. Different Top and Bottom, but same Powers.The Expanding Quotients Rule can alsobe used in reverse, to make a fractionwith IDENTICAL POWERS into asingle bracketed exponent Fraction.
• 10. For Expanding Quotients Rule BACKWARDS, we have two differentbases, BUT THEY MUST BOTH BE RAISED TO THE SAME POWER.62626 222222= = = (3)2or 9h3h3h 3h 343434 4= = =a7a7a 7a 7c7c7c c= = =