Answer:
A. [tex]9\cdot 9^{x-1}[/tex]
C. [tex](\frac{36}{4})^x[/tex]
Step-by-step explanation:
Given:
The given expression is [tex]9^x[/tex]
Let us simplify each choice and check whether they simplify to [tex]9^x[/tex] or not.
Choice A:
[tex]9\cdot 9^{x-1}[/tex]
We use the law of indices: [tex]a^m\cdot a^n=a^{m+n}[/tex]
Therefore, [tex]9^1\cdot 9^{x-1}=9^{1+x-1}=9^x=9^x(True)[/tex]
Choice B:
[tex]9\cdot 9^{x+1}[/tex]
We use the law of indices: [tex]a^m\cdot a^n=a^{m+n}[/tex]
Therefore, [tex]9^1\cdot 9^{x+1}=9^{1+x+1}=9^{x+2}\ne 9^x(False)[/tex]
Choice C:
[tex](\frac{36}{4})^{x}[/tex]
We simplify the fraction inside the parenthesis. So,
[tex](\frac{36}{4})^{x}=(9)^x=9^x(True)[/tex]
Choice D:
[tex]x^5\ne 9^x[/tex]
Choice E:
[tex]36\ne 9^x[/tex]
Therefore, the correct options are A and C.
