Question

Which expressions are equivalent to the one below? Check all that apply. 3^x A. 3 • 3^x + 1 B. 3 • 3^x - 1 C.18^x/3 D.(18/6)^x E. x^3 F.18^x/16^x

Answer 1

B, D, F

Explanation:

`Use\\\\a^n\cdot a^m=a^(n+m)\\\\(a^n)/(b^n)=\left((a)/(b)\right)^n\\=================\\A.\ 3^(x+1)=3^x\cdot 3\\eq3^x\\\\B.\ 3\cdot3^(x-1)=3\cdot3^x\cdot3^(-1)=(3^1\cdot3^(-1))\cdot3^x=3^(1+(-1))\cdot3^x=3^0\cdot3^x=1\cdot3^x=3^x\\\\C.\ (18^x)/(3)\\eq3^x\\\\D.\ \left((18)/(6)\right)^x=(3)^x=3^x\\\\E.\ x^3\\eq3^x\\\\F.\ (18^x)/(6^x)=\left((18)/(6)\right)^x=(3)^x=3^x`