Respuesta :
Answer:
options: A,C,E are correct.
Step-by-step explanation:
We have to find the expression equivalent to the expression:
[tex]\dfrac{21^x}{3^x}[/tex]
we know that: [tex]21^x=(3\times7)^x\\\\21^x=3^x\times7^x[/tex]
Hence,
[tex]\dfrac{21^x}{3^x}=\dfrac{3^x\times7^x}{3^x}=7^x[/tex]-----(1)
A) [tex](\dfrac{21}{3})^x= 7^x[/tex] (same as(1))
Hence, option A is correct.
B) 7 ; which is a different expression from (1)
Option B is incorrect.
C) [tex]7^x[/tex] (Same as (1))
Option C is correct.
D) [tex](21-3)^x=18^x[/tex] which is a different expression from (1)
Hence, option D is incorrect.
E) [tex]\dfrac{7^x\times3^x}{3^x}=7^x[/tex] ; which is same as (1)
Hence, Option E is correct.
F) [tex]3^x[/tex] ; which is not same as expression (1)
Hence, option F is incorrect.
Answer:
(A), (C) and (E)
Step-by-step explanation:
The given expression is:
[tex]\frac{21^x}{3^x}[/tex]
(A) The expression is:
[tex](\frac{21}{3})^x[/tex]
Now, this expression can be written as:
[tex]\frac{21^x}{3^x}[/tex]
which is equivalent to the given expression, thus this option is correct.
(B) The expression is:
[tex]7[/tex]
The above given expression that is [tex]\frac{21^x}{3^x}[/tex] can be written as:
[tex]\frac{(7\times3)^x}{3^x}=7^x[/tex] which is not equivalent, thus this option is incorrect.
(C) The given expression is:
[tex]7^x[/tex]
The above given expression that is [tex]\frac{21^x}{3^x}[/tex] can be written as:
[tex]\frac{(7\times3)^x}{3^x}=7^x[/tex] which is equivalent, thus this option is correct.
(D) The given expression is:
[tex](21-3)^x[/tex]
which can be solved as [tex]18^x[/tex] which is not equivalent to the given expression, therefore this option is incorrect.
(E) The given expression is:
[tex]\frac{7^x\times3^x}{3^x}[/tex]
which can be written as:
[tex]\frac{21^x}{3^x}[/tex] which is equivalent to the given expression, thus this option is correct.
(F) The given expression is:
[tex]3^x[/tex]
which is not equivalent to the given expression, thus this option is incorrect.
