Which expressions are equivalent to the one below? Check all that apply. 21^x/3^xA.(21/3)^x B.7C.7^xD.(21 - 3)^xE.7^x*3^x/3^x F.3^x

Accepted Solution

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.