Question

Which expressions are equivalent to the one below? Check all that apply. 212 32

Answer 1

Given:

`(21^x)/(3^x)`

Aim:

We need to find the equivalent expression for the given expression.

Step-by-step explanation:

`Use\text{ }(a^n)/(b^n)=((a)/(b))^n.\text{ Here a=21, b=3 and n=x.}`

`(21^x)/(3^x)=((21)/(3))^x`
`Use\text{ 21=7}*3\text{ in the given expression.}`

`(21^x)/(3^x)=((7*3)^x)/(3^x)`
`Use\text{ }(a* b)^x=a^x* b^x.\text{ Here a=7, b=3 and n=x.}`

`(21^x)/(3^x)=(7^x*3^x)/(3^x)`

Cancel out common terms.

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

Final answer:

`B.(7^x*3^x)/(3^x)`

`C.\text{ }7^x`

`D.\text{ }((21)/(3))^x`