Oblicz. a) [tex]\frac{4^{5} *3^{5} *7}{6^{4} *32}[/tex] b) [tex]\frac{12^{5}*2^{5} *5 }{4^{6}*9^{2} .... Question from @thisismebicz

April 2022 1 8 Report

Oblicz.
a) [tex]\frac{4^{5} *3^{5} *7}{6^{4} *32}[/tex]
b) [tex]\frac{12^{5}*2^{5} *5 }{4^{6}*9^{2} }[/tex]
c) [tex]\frac{10^{12}*15^{11} *6^{10} }{30^{9} *5^{14}*2^{13} *3^{12} }[/tex]
d) [tex]\frac{12*30^{12} *10^{7} }{10*6^{13}*25^{9}*8^{3} }[/tex]

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kamci04

Odpowiedź:

$\frac{ {4}^{5} \times {3}^{5} \times 7}{ {6}^{4} \times 32} = \frac{(4 \times 3) ^{5} \times 7}{1296 \times 32} = \frac{ {12}^{5} \times 7}{1296 \times 32} = \frac{248832 \times 7}{1296 \times 32} = \frac{192 \times 7}{32} = 6 \times 7 = 42$

$\frac{ {12}^{5} \times {2}^{5} \times 5 }{ {4}^{6} \times {9}^{2} } = \frac{(12 \times 2)^{5} \times 5}{4096 \times 81} = \frac{24^{5} \times 5}{4096 \times 81} = \frac{7962624 \times 5}{4096 \times 81} = \frac{1944 \times 5}{81} = 24 \times 5 = 120$

$\frac{ {10}^{12} \times {15}^{11} \times {6}^{10} }{ {30}^{9} \times {5}^{14} \times {2}^{13} \times {3}^{12} } = \frac{(10 \times 15 \times 6) ^{10} \times {10}^{2} \times 15 }{(30 \times 5 \times 2 \times 3)^{9} \times {5}^{5} \times {2}^{4} \times {3}^{3} } = \frac{ {900}^{10} \times 1500}{ {900}^{9} \times 3125 \times 16 \times 27} = \frac{900 \times 1500}{1350000} = \frac{900}{900} = 1$

$\frac{12 \times {30}^{12} \times {10}^{7} }{10 \times {6}^{13} \times {25}^{9} \times {8}^{3} } = \frac{12 \times (30 \times 10) ^{7} \times {30}^{5} }{10 \times (6 \times 25 \times 2)^{9} \times {6}^{4} } = \frac{12 \times {300}^{7} \times {30}^{5} }{10 \times {300}^{9} \times {6}^{4} } = \frac{12 \times 24300000}{10 \times 90000 \times 1296} = \frac{12 \times 270}{10 \times 1296} = \frac{3240 }{12960} = \frac{1}{4}$