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Lời giải:
a. $2^3.8=2^3.2^3=2^6$
b. $5^2.25=5^2.5^2=5^4$
c. $27:3^2=3^3:3^2=3^1$
d. $4^2.16=4^2.4^2=4^4$
e. $5^3.5^6=5^9$
f. $3^4.3=3^5$
g.$3^5.4^5=(3.4)^5=12^5$
h. $8^5.2^3=(2^3)^5.2^3=2^{15}.2^3=2^{18}$
i. $a^3.a^5=a^8$
j. $x^7.x.x^4=x^{7+1+4}=x^{12}$
k. $5^6:5^3=5^3$
l. $3^{15}:3^3=3^{15-3}=3^{12}$
m. $4^6:4^6=4^0=1$
n. $9^8:3^2=(3^2)^8:3^2=3^{16}:3^2=3^{14}$
o. $a:a=a^0=1$
p. $5^8.5.5^2=5^{8+1+2}=5^{11}$
q. $4.4^3=4^4$
r. $3.3^4=3^5$
s. $36.6^5=6^2.6^5=6^7$
t. $2^5.2^3=2^8$
u. $3^{10}:3^3=3^7$
v. $2^{10}:2^3=2^7$
w. $5^8:25=5^8:5^2=5^6$
x. $16:2^3=2^4:2^3=2^1$
y. $4.2^3=2^2.2^3=2^5$
z. $2^{10}:4=2^{10}:2^2=2^8$
`@` `\text {Ans}`
`\downarrow`
`j)`
\(x^{17}\div x^{12}=x^{17-12}=x^5\)
`k)`
\(x^8\div x^5=x^{8-5}=x^3\)
`r)`
\(a^5\div a^5=a^{5-5}=a^0=1\)
`l)`
\(x^4\div x=x^{4-1}=x^3\)
`m)`
\(x^7\div x^6=x^{7-6}=x\)
`n)`
\(x^9\div x^9=x^{9-9}=x^0=1\)
`o)`
\(a^{12}\div a^5=a^{12-5}=a^7\)
`p)`
\(a^8\div a^6=a^{8-6}=a^2\)
`q)`
\(a^{10}\div a^7=a^{10-7}=a^3\)
`r(2),`
\(1024\div4=2^{10}\div2^2=2^8\)
`t)`
\(512\div2^3=2^9\div2^3=2^6\)
1/51+1/52+1/53+....+1/100>1/100+1/100+1/100+...+1/100(50 so 0)=50/100=1/2
\(\dfrac{2n+15}{n+1}\in Z\Rightarrow2n+15⋮n+1\)
\(\Rightarrow2n+15-2\left(n+1\right)⋮n+1\)
\(\Rightarrow13⋮n+1\)
\(\Rightarrow n+1=Ư\left(13\right)\)
\(\Rightarrow n+1=\left\{-13;-1;1;13\right\}\)
\(\Rightarrow n=\left\{-14;-2;0;12\right\}\)
Cách hai: Theo bezout ta có: \(\dfrac{2n+15}{n+1}\) \(\in\) Z ⇔ 2.(-1) + 15 ⋮ n +1
⇔ 13 ⋮ n +1 ⇒ n + 1 \(\in\) { -13; -1; 1; 13} ⇒ n \(\in\) { -14; -2; 0; 12}
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