Question

arata daca (7^4+7^5)×49 este cub perfect

Answer 1

(7^4+7^5)×49 = (7^4+7^5)×7^2 = 7^6+7^7 = 7^6(1+7)=8*7^6 =(2^1)^3*(7^2)^3

Answer 2

( 7⁴ + 7⁵ ) x 49 =  98³

= ( 7⁴ x 1 + 7⁴ x 7 ) x 7² =

= 7⁴ x ( 1 + 7 ) x 7² =

= 7⁴ x 7² x 8 =

= 7 ⁽ ⁴ ⁺ ² ⁾  x 2³ =

= 7⁶ x 2³ =       7⁶ = ( 7² ) ³

= ( 7² x 2 )³ =

= ( 49 x 2 )³ =

= 98³ → cub perfect