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

A.(21-3)^x
B.7
C.7^x
D.(21/3)^x
E.7^x*3^x/3^x
F.3^x

2 Answers

5 votes
C and E and F are all the correct answers
User Igelineau
by
5.9k points
2 votes

Answer:

The equivalent expressions are:

C.


7^x

D.


((21)/(3))^x

E.


(7^x\cdot 3^x)/(3^x)

Explanation:

We are asked to find the algebraic expression that is equivalent to the expression:


(21^x)/(3^x)

A)


(21-3)^x

We know that this expression is incorrect.

Since,
(a^x)/(b^x)\\eq (a-b)^x

B)

7

This option is also incorrect.

Since,


(21^x)/(3^x)=((21)/(3))^x\\\\(21^x)/(3^x)=7^x

C)


7^x

This option is true.

Since,


(21^x)/(3^x)=((21)/(3))^x\\\\(21^x)/(3^x)=7^x

D)


((21)/(3))^x

This option is true.

Since,


(a^x)/(b^x)=((a)/(b))^x

E)


(7^x\cdot 3^x)/(3^x)

This option is correct.

Since,


(21^x)/(3^x)=((7\cdot 3)^x)/(3^x)=(7^x\cdot 3^x)/(3^x)

F)


3^x

This option is incorrect.

Since we get a expression as:


7^x but not
3^x

User Salma Gomaa
by
5.9k points