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Firdavs [7]
3 years ago
10

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

Mathematics
2 answers:
sasho [114]3 years ago
6 0

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.

satela [25.4K]3 years ago
5 0

Answer:

<em>options:  A,C,E </em>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.

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