Question

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

Answer 1

Answer:

The equivalent expressions are:

C.

$7^x$

D.

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

E.

$\dfrac{7^x\cdot 3^x}{3^x}$

Step-by-step explanation:

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

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

A)

$(21-3)^x$

We know that this expression is incorrect.

Since, $\dfrac{a^x}{b^x}\neq (a-b)^x$

B)

7

This option is also incorrect.

Since,

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

C)

$7^x$

This option is true.

Since,

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

D)

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

This option is true.

Since,

$\dfrac{a^x}{b^x}=(\dfrac{a}{b})^x$

E)

$\dfrac{7^x\cdot 3^x}{3^x}$

This option is correct.

Since,

$\dfrac{21^x}{3^x}=\dfrac{(7\cdot 3)^x}{3^x}=\dfrac{7^x\cdot 3^x}{3^x}$

F)

$3^x$

This option is incorrect.

Since we get a expression as:

$7^x$ but not $3^x$

Answer 2

C and E and F are all the correct answers