Question

Stabiliți dacă a) 9 la puterea 7 si 4 la puterea 3 sunt pătrate perfecte
b) (7 la putera 4 + 7 la puterea 5) x 49 este cub perfect.

Answer 1

$a) {9}^{7} = {( {3}^{2}) }^{7} = {( {3}^{7}) }^{2} = > p.p$

${4}^{3} = { ({2}^{2}) }^{3} = { ({2}^{3}) }^{2} = > p.p$

$b)( {7}^{4} + {7}^{5} ) \times 49$

$=( {7}^{4} + {7}^{5} ) \times {7}^{2}$

$= {7}^{4} \times {7}^{2} + {7}^{5} \times {7}^{2}$

$= {7}^{4 + 2} + {7}^{5 + 2}$

$= {7}^{6} + {7}^{7}$

$= {7}^{6} (1 + 7)$

$= {7}^{6} \times 8$

$= {7}^{6} \times {2}^{3}$

$= { ({7}^{2} )}^{3} \times {2}^{3}$

$= { ({7}^{2} \times 2) }^{3} = > c.p$