Answer:
The equivalent expressions are:
C.
[tex]7^x[/tex]
D.
[tex](\dfrac{21}{3})^x[/tex]
E.
[tex]\dfrac{7^x\cdot 3^x}{3^x}[/tex]
Step-by-step explanation:
We are asked to find the algebraic expression that is equivalent to the expression:
[tex]\dfrac{21^x}{3^x}[/tex]
A)
[tex](21-3)^x[/tex]
We know that this expression is incorrect.
Since, [tex]\dfrac{a^x}{b^x}\neq (a-b)^x[/tex]
B)
7
This option is also incorrect.
Since,
[tex]\dfrac{21^x}{3^x}=(\dfrac{21}{3})^x\\\\\dfrac{21^x}{3^x}=7^x[/tex]
C)
[tex]7^x[/tex]
This option is true.
Since,
[tex]\dfrac{21^x}{3^x}=(\dfrac{21}{3})^x\\\\\dfrac{21^x}{3^x}=7^x[/tex]
D)
[tex](\dfrac{21}{3})^x[/tex]
This option is true.
Since,
[tex]\dfrac{a^x}{b^x}=(\dfrac{a}{b})^x[/tex]
E)
[tex]\dfrac{7^x\cdot 3^x}{3^x}[/tex]
This option is correct.
Since,
[tex]\dfrac{21^x}{3^x}=\dfrac{(7\cdot 3)^x}{3^x}=\dfrac{7^x\cdot 3^x}{3^x}[/tex]
F)
[tex]3^x[/tex]
This option is incorrect.
Since we get a expression as:
[tex]7^x[/tex] but not [tex]3^x[/tex]
