Question

Which expressions are equivalent to the one below? Check all that apply.

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

Answer 1

`A.\;\; \left((21)/(3)\right)^x\\\\\\C. \;\;(7^(x)\cdot3^(x))/(3^(x))\\\\E. \;\;7^x`

Explanation:

`(21^x)/(3^x) = \left((21)/(3)\right)^x`
`21 = 7 \cdot 3\\\\So\; (21^x)/(3^x) = (7^x \cdot 3^x)/(3^x)`
So choice A is correct

`------------------------`

`21 = 7 \cdot 3\\\\So\; (21^x)/(3^x) \\\\\\= ((7\cdot3)^(x))/(3^(x))=(7^(x)\cdot3^(x))/(3^(x))`

So Choice C is correct

`------------------`

`\text{SInce $(21)/(3) = 7$}\\\\\text{ $\left((21)/(3) \right)^x = (7)^x = 7^x$}`

Therefore choice E is correct

All the other three are incorrect