Simplify This

Number Theory Level 1

Simplify :

6 2007 − 6 2006 30 \large\dfrac{6^{2007}-6^{2006}}{30}

6 2005 6^{2005} 6 2007 6^{2007} 6 2006 6^{2006}

Anuj Shikarkhane by Anuj Shikarkhane , 19, India

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3 solutions

Mohammad Khaza
Feb 9, 2018

6 2007 − 6 2006 30 \dfrac{6^{2007}-6^{2006}}{30}

= 6 2006 ( 6 1 − 6 0 ) 5 × 6 \dfrac{{6^{2006}} (6^1-6^0)}{5\times 6}

= 6 2006 . 5 5 × 6 \dfrac{6^{2006} . 5}{5 \times 6}

= 6 2006 × 6 − 1 6^{2006} \times 6^{-1}

= 6 2005 6^{2005}

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6 2007 − 6 2006 30 = 6 2006 ( 6 − 1 ) 30 = 6 2006 ( 5 ) 30 = 6 2006 6 = 6 2006 − 1 = 6 2005 \dfrac{6^{2007}-6^{2006}}{30}=\dfrac{6^{2006}(6-1)}{30}=\dfrac{6^{2006}(5)}{30}=\dfrac{6^{2006}}{6}=6^{2006-1}=6^{2005}

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Siva Budaraju
Sep 10, 2017

6 2007 − 6 2006 30 \frac{6^{2007}-6^{2006}}{30} = = 6 • 6 2006 − 6 2006 30 \frac{6•6^{2006}-6^{2006}}{30} = = 5 • 6 2006 30 \frac{5•6^{2006}}{30} = = 6 2006 6 \frac{6^{2006}}{6} = 6 2005 = 6^{2005}

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