soal perpangkatan 1

\frac{3^{2008} \left ( 10^{2013}+5^{2012} \cdot 2^{2011}\right )}{5^{2012} \left ( 6^{2010}+3^{2009} \cdot 2^{2008}\right )}=...

Solusinya

\frac{3^{2008} \left ( 10^{2013}+5^{2012} \cdot 2^{2011}\right )}{5^{2012} \left ( 6^{2010}+3^{2009} \cdot 2^{2008}\right )} = \frac{3^{2008} \left ( (5 \cdot 2)^{2013}+5^{2012} \cdot 2^{2011}\right )}{5^{2012} \left ( (3 \cdot 2)^{2010}+3^{2009} \cdot 2^{2008}\right )}

= \frac {3^{2008} \left ( 5^{2013} \cdot 2^{2013}+5^{2012} \cdot 2^{2011}\right )}{5^{2012} \left ( 3^{2010} \cdot 2^{2010}+3^{2009} \cdot 2^{2008}\right )}

= \frac {3^{2008} \left ( 5^{2012} \cdot 2^{2011} \left [ 5 \cdot 2^{2} + 1\right ]\right )}{5^{2012} \left ( 3^{2009} \cdot 2^{2008} \left [ 3 \cdot 2^{2} + 1\right ] \right )}

= \frac {3^{2008} \left ( 5^{2012} \cdot 2^{2011} \left [ 5 \cdot 4 + 1\right ]\right )}{5^{2012} \left ( 3^{2009} \cdot 2^{2008} \left [ 3 \cdot 4 + 1\right ] \right )}

= \frac {3^{2008} \left ( 5^{2012} \cdot 2^{2011} \left [ 21\right ]\right )}{5^{2012} \left ( 3^{2009} \cdot 2^{2008} \left [ 13\right ] \right )}

= \frac {3^{2008} \left ( 5^{2012} \cdot 2^{2011} \left [ 3 \cdot 7\right ]\right )}{5^{2012} \left ( 3^{2009} \cdot 2^{2008} \left [ 13\right ] \right )}

= \frac {2^{2011} \cdot 3^{2008} \cdot 3 \cdot 5^{2012} \cdot 7}{2^{2008} \cdot 3^{2009} \cdot 5^{2012} \cdot 13}

= \frac {2^{2011} \cdot 3^{2009} \cdot 5^{2012}\cdot 7}{2^{2008}\cdot 3^{2009} \cdot 5^{2012} \cdot 13}

= \frac {2^{3} \cdot 7}{13}

= \frac {8 \cdot 7}{13}

= \frac {56}{13}

powerpoint:

http://www.mediafire.com/?snfkrjz95xl92e7 –>2007
http://www.mediafire.com/?gqqtkily8az2yxe –>2010

Videonya

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