Toán Lớp 7: Tính hợp lí: `a)(0,25)^3 . 32` `b)(81^11 . 3^17)/(27^10. 9^15)` `c)(4^(2).25^(2)+32.125)/(2^(3).5^(2)`

Question

Toán Lớp 7:  Tính hợp lí: a)(0,25)^3 . 32 b)(81^11 . 3^17)/(27^10. 9^15) c)(4^(2).25^(2)+32.125)/(2^(3).5^(2)

maianhnhiquynh · Answer

a)   (0,25)^3 . 32   =  (0,25)^2 . 0,25  . 32   =  1/16 . 8   = 1/2   b)   (81^{11} . 3^{17})/(27^{10} . 9^{15})   = ( (3^4)^{11} . 3^17)/( (3^3)^{10} . (3^2)^{15})   = (3^44 . 3^17)/(3^30 . 3^30)   =  (3^61)/(3^60)    = 3   c)   (4^2 . 25^2 + 32 . 125)/(2^3 . 5^2)    = ( (2^2)^2 . (5^2)^2 + 2^5 . 5^3)/(2^3 . 5^2)   =  (2^4 . 5^4 + 2^5 . 5^3)/(2^3 . 5^2)    = (2^4 . 5^3 . (5 +2))/(2^3 . 5^2)    = 2 . 5 . (5+2)   =  10 . 7    = 70

dantam45 · Answer

a) ( 0,25 )^3 . 32   = ( 1/4 )^3 . 32   = 1/64 . 32   = 1/2   b) ( 81^11 . 3^17 )/( 27^10 . 9^15 )   = ( ( 3^4 )^11 . 3^17 )/( ( 3^3 )^10 . ( 3^2 )^15 )   = ( 3^44 . 3^17 )/( 3^30 . 3^30 )   = ( 3^61 )/( 3^60 ) = 3   c, ( 4^2 . 25^2 + 32 . 125 )/( 2^3 . 5^2 )   = ( 2^4 . ( 5^2 )^2 + 2^5 . 5^3 )/( 2^3 . 5^2 )   = ( 2^4 . 5^4 + 2^5 . 2 . 5^3 )/( 2^3 . 5^2 )   = ( 2^4 . ( 5^4 + 5^3 . 2 ) )/( 2^3 . 5^2 )   = ( 2 . ( 5^3 . 5 + 5^3 . 2 ) )/( 5^2 )   = ( 2 . 5^3 . ( 5 + 2 ) )/( 5^2 )   = 2 . 5 . 7   = 10 . 7   = 70