Question

Which expressions are equivalent to the one below? Check all that apply. 21^x/3^x

Answer 1

Answer:

(A), (C) and (E)

Step-by-step explanation:

The given expression is:

$\frac{21^x}{3^x}$

(A) The expression is:

$(\frac{21}{3})^x$

Now, this expression can be written as:

$\frac{21^x}{3^x}$

which is equivalent to the given expression, thus this option is correct.

(B) The expression is:

$7$

The above given expression that is $\frac{21^x}{3^x}$ can be written as:

$\frac{(7\times3)^x}{3^x}=7^x$ which is not equivalent, thus this option is incorrect.

(C) The given expression is:

$7^x$

The above given expression that is $\frac{21^x}{3^x}$ can be written as:

$\frac{(7\times3)^x}{3^x}=7^x$ which is equivalent, thus this option is correct.

(D) The given expression is:

$(21-3)^x$

which can be solved as $18^x$ which is not equivalent to the given expression, therefore this option is incorrect.

(E) The given expression is:

$\frac{7^x\times3^x}{3^x}$

which can be written as:

$\frac{21^x}{3^x}$ which is equivalent to the given expression, thus this option is correct.

(F) The given expression is:

$3^x$

which is not equivalent to the given expression, thus this option is incorrect.

Answer 2

Answer:

options:  A,C,E are correct.

Step-by-step explanation:

We have to find the expression equivalent to the expression:

$\dfrac{21^x}{3^x}$

we know that: $21^x=(3\times7)^x\\\\21^x=3^x\times7^x$

Hence,

$\dfrac{21^x}{3^x}=\dfrac{3^x\times7^x}{3^x}=7^x$-----(1)

A)   $(\dfrac{21}{3})^x= 7^x$  (same as(1))

Hence, option A is correct.

B)  7 ; which is a different expression from (1)

Option B is incorrect.

C) $7^x$   (Same as (1))

Option C is correct.

D) $(21-3)^x=18^x$   which is a different expression from (1)

Hence, option D is incorrect.

E) $\dfrac{7^x\times3^x}{3^x}=7^x$   ; which is same as (1)

Hence, Option E is correct.

F) $3^x$  ; which is not same as expression (1)

Hence, option F is incorrect.