MATH SOLVE

5 months ago

Q:
# Which expressions are equivalent to the one below? Check all that apply. 27^x/9^x

Accepted Solution

A:

Answer: The correct options are(B) [tex]\dfrac{9^x.3^x}{9^x}[/tex](C) [tex] 3^x[/tex](E) [tex]\left(\dfrac{27}{9}\right)^3.[/tex] Step-by-step explanation: The given expression is[tex]E=\dfrac{27^x}{9^x}.[/tex]We are to select the correct expressions that are equivalent to the expression "E".We will be using the following properties of exponents:[tex](i)~a^x.b^x=(ab)^x,\\\\(ii)~\dfrac{a^x}{b^x}=\left(\dfrac{a}{b}\right)^x.[/tex]We have[tex]E\\\\\\=\dfrac{27^x}{9^x}\\\\\\=\dfrac{(9\times 3)^x}{9^x}\\\\\\=\dfrac{9^x.3^x}{9^x}\\\\\\=3^x.[/tex]Also,[tex]E=\dfrac{27^x}{9^x}=\left(\dfrac{27}{9}\right)^x.[/tex]Thus, (B), (C) and (E) are the correct options.