Tính giá trị biểu thức :
`b, (3.4^{2}.2^{7})^{2} : (3^{2}.2^{20})`
`c, (2^{3}.9^{4} + 9^{3}.45) : (9^{2}.10 – 9^{2})`
`d, 24^{4} : 3^{4} – 32^{12} : 16^{12}`
`e, (2^{9}.3 + 2^{9}.5) : 2^{12}`
Tính giá trị biểu thức :
`b, (3.4^{2}.2^{7})^{2} : (3^{2}.2^{20})`
`c, (2^{3}.9^{4} + 9^{3}.45) : (9^{2}.10 – 9^{2})`
`d, 24^{4} : 3^{4} – 32^{12} : 16^{12}`
`e, (2^{9}.3 + 2^{9}.5) : 2^{12}`
$b$) $\dfrac{(3.4^2 . 2^7)^2}{3^2 . 2^{20}}$
$= \dfrac{3^2 . 2^{22}}{3^2. 2^{20}}$
$= 2^2 = 4$
$c$) $\dfrac{2^3 . 9^4 + 9^3 . 45}{9^2 . 10 – 9^2}$
$= \dfrac{2^3 . 3^8 + 3^8 . 5}{3^4 . 10 – 3^4}$
$= \dfrac{3^8 . (8 + 5)}{3^{4}.(10-1)}$
$= 3^2 . 13 = 117$
$d$) $24^4 : 3^4 – 32^{12} : 16^{12}$
$= (24:3)^4 – (32:16)^{12}$
$= 8^4 – 2^{12}$
$= 2^{12} – 2^{12}$
$= 0$
$e$) $\dfrac{2^9 . 3 + 2^9 . 5}{2^{12}}$
$= \dfrac{2^9.(3+5)}{2^{12}}$
$= \dfrac{2^{12}}{2^{12}}$
$= 1$
Giải thích các bước giải:
b) ( 3 . 4² . $2^{7}$ )² : ( 3² . $2^{20}$ )
= ( 3 . 16 . 128 )² : ( 9 . 1048576 )
= ( 48 . 128 )² : 9437184
= 6144² : 9437184
= 37748736 : 9437184
= 4
c) ( 2³ . $9^{4}$ + 9³ . 45 ) : ( 9² . 10 – 9² )
= ( 8 . 6561 + 729 . 45 ) : ( 81 . 10 – 81 )
= ( 52488 + 32805 ) : ( 810 – 81 )
= 85293 : 729
= 117
d) $24^{4}$ : $3^{4}$ – $32^{12}$ : $16^{12}$
= 4096 – 4096
= 0
e) ( $2^{9}$ . 3 + $2^{9}$ . 5 ) : $2^{12}$
= $2^{9}$ . ( 3 + 5 ) : $2^{12}$
= $2^{9}$ . 8 : $2^{12}$
= $2^{9}$ . 2³ : $2^{12}$
= $2^{12}$ : $2^{12}$
= 1