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:

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

Now, notice that:

$9=\frac{36}{4}.$

Therefore:

$9^x=(\frac{36}{4})^x.$

Using the first property we get that:

$9^x=\frac{36^x}{4^x}.$

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

$9^x=9^{1+x-1}=9*9^{x-1}.$

Answer: Options A, E, and F.