Question

Which expressions are equivalent to the one below. Check all that apply. 16^x

Answer 1

`A.\ 4^x\cdot4^x=4^(x+x)=4^(2x)\qquad\text{used}\ a^n\cdot a^m=a^(n+m)\\\\B.\ 4^(2x)=(4^2)^x=16^x\qquad\text{used}\ (a^n)^m=a^(nm)\\\\C.\ 4^2\cdot4^x=4^(2+x)\\\\D.\ (4\cdot4)^x=16^x\\\\E.\ 4\cdot4^(2x)=4^(1+2x)\\\\F.\ 4\cdot4^x=4^(1+x)\\\\Answer:\ \boxed{B.\ and\ D.}`