[tex] A.\ \dfrac{15^x}{3^x}=\left(\dfrac{15}{3}\right)^x=(5)^x=5^x\\\\Used\ \left(\dfrac{a}{b}\right)^n=\dfrac{a^n}{b^n}\\\\D.\ \left(\dfrac{15}{3}\right)^x=(5^x)=5^x\\\\E.\ 5\cdot5^{x-1}=5^1\cdot5^{x-1}=5^{1+x-1}=5^x\\\\Used\ a^n\cdot a^m=a^{n+m}\\\\Answer:\ A,\ D\ and\ E. [/tex]
