Question

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

9^x
ОА. 9. 9x - 1
В. 9. 9х+1
с. 36/4^x
D.x^5
Е. 36
​

Answer 1

A.
`9\cdot 9^(x-1)`

C.
`((36)/(4))^x`

Explanation:

Given:

The given expression is
`9^x`

Let us simplify each choice and check whether they simplify to
`9^x` or not.

Choice A:

`9\cdot 9^(x-1)`

We use the law of indices:
`a^m\cdot a^n=a^(m+n)`

Therefore,
`9^1\cdot 9^(x-1)=9^(1+x-1)=9^x=9^x(True)`

Choice B:

`9\cdot 9^(x+1)`

We use the law of indices:
`a^m\cdot a^n=a^(m+n)`

Therefore,
`9^1\cdot 9^(x+1)=9^(1+x+1)=9^(x+2)\\e 9^x(False)`

Choice C:

`((36)/(4))^(x)`

We simplify the fraction inside the parenthesis. So,

`((36)/(4))^(x)=(9)^x=9^x(True)`

Choice D:

`x^5\\e 9^x`

Choice E:

`36\\e 9^x`

Therefore, the correct options are A and C.