Question

Which expressions are equivalent to the one below? Check all that apply. 9x 36* D A Св. х5 B. | * c. c. 36 D D. 9.9X+1 36 DE E. LASSE F. 9.9x-1

Answer 1

To answer this question we will use the following properties of exponents:

`\begin{gathered} ((a)/(b))^x=(a^x)/(b^x), \\ a^x*a^y=a^(x+y). \end{gathered}`

Now, notice that:

`9=(36)/(4).`

Therefore:

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

Using the first property we get that:

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

Now, notice that x=1+x-1, then:

`9^x=9^(1+x-1)=9*9^(x-1).`

Answer: Options A, E, and F.