Question

!DAU COROANA!
7. Simplifica fractiile:
a. 5²⁹/5²⁷
b. 25²⁹/125¹⁸
c. 5⁴⁴+5⁴⁴/5⁴⁴
d. 4¹⁰+8⁷/2²²-16⁵
e. 3³+3⁴/12³
f. 1+2+3+...+23+24/2+4+6+...+46+48​

Answer 1

$a) \: \frac{ {5}^{29} }{ {5}^{27} } = {5}^{29 - 27} = {5}^{2} \\ b) \: \frac{ {25}^{29} }{ {125}^{18} } = \frac{ {({5}^{2})}^{29} }{ ( { {5}^{3}) }^{18} } = \frac{ {5}^{58} }{ {5}^{54} } = {5}^{4} \\ c) \frac{ {5}^{44} + {5}^{44} }{ {5}^{44} } = \frac{2 \times {5}^{44} }{ {5}^{44} } = 2 \: ( se \: simplifica \: {5}^{44} )$

$d) \frac{ {4}^{10} + {8}^{7}}{{2}^{22} - {16}^{5} } = \frac{ {( {2}^{2} )}^{10} + {( {2}^{3} )}^{7} }{ {2}^{22} - {( {2}^{4} )}^{5} } = \frac{ {2}^{20} + {2}^{21} }{ {2}^{22} - {2}^{20} } = \frac{ {2}^{20}(1 + 2) }{ {2}^{20} ( 4 - 1)} = \frac{3}{3} = 1 \\ e) \frac{ {3}^{3} + {3}^{4} }{ {12}^{3} } = \frac{ {3}^{3} (1 + 3) }{ {(3 \times 4)}^{3} } = \frac{ {3}^{3} \times 4 }{ {3}^{3} \times {4}^{3} } = \frac{4}{ {4}^{3} } = {4}^{ - 2}$

$f) \: \frac{1 + 2 + 3 + ... + 23 + 24}{2 + 4 + 6 + ... + 46 + 48} = \frac{1 + 2 + 3 + ... + 23 + 24}{2(1 + 2 + 3 + ... + 23 + 24)} = \frac{1}{2}$Dacă ești pe telefon, glisează în stânga sau dreapta pentru a vedea tot.