\(\large\begin{array}{l}\mathsf{\dfrac{1}{16}=0.0625~~~~\checkmark}\end{array}\)
The definitions:
\(\large\begin{array}{l}\fbox{$\mathsf{a^a\cdot a^b=a^{a+b}$ }}\\\\\\\mathsf{~So...}\\\\\\\mathsf{~4^3\cdot 4^{-5}\Leftrightarrow4^{3+(-5)}\Leftrightarrow4^{3-5}\Leftrightarrow~4^{-2}\Leftrightarrow\dfrac{1}{4^2}\Leftrightarrow\dfrac{1}{16}}~~~~\checkmark\end\)
\(\large\begin{array}{l}\fbox{$\mathsf{a^{-b}=\dfrac{1}{a^b}}$}\\\\\\\mathsf{So...}\\\\\\\mathsf{4^{-2}~\Leftrightarrow~\dfrac{1}{4^2} }~\Leftrightarrow~\dfrac{1}{16}~~~~\checkmark\end{array}\)
\(\large\begin{array}{l}\fbox{$\mathsf{a^{-1}=\dfrac{1}{a}}$}\\\\\\\mathsf{So...}\\\\\\\mathsf{16^{-1}=\dfrac{1}{16}}~~~~\checkmark\end{array}\)
\(\large\begin{array}{l}\fbox{$\mathsf{\begin{pmatrix}\dfrac{a}{b}\end{pmatrix}^2= \dfrac{a^2}{b^2}}$}\\\\\\\mathsf{So...}\\\\\\\mathsf{\begin{pmatrix} \dfrac{1}{4} \end{pmatrix}^2~\Leftrightarrow~\dfrac{1^2}{4^2}~\Leftrightarrow~ \dfrac{1}{16}}~~~~\checkmark\end{array}\)
\(\large\begin{array}{l}\fbox{$\mathsf{(a^b)^c=a^{b\cdot c}}$}\\\\\\\mathsf{So...}\\\\\\\mathsf{(4^{-1})^2~\Leftrightarrow~4^{(-1)\cdot 2}~\Leftrightarrow~4^{-2}~\Leftrightarrow~\dfrac{1}{4^2}~\Leftrightarrow~ \dfrac{1}{16}~~~~\checkmark}\end{array}\)
\(\large\begin{array}{l}\fbox{$\mathsf{\dfrac{a^b}{a^c}=a^{b-c}}$}\\\\\\\mathsf{So...}\\\\\\\mathsf{\dfrac{4^3}{4^5}~\Leftrightarrow~4^{3-5}~\Leftrightarrow~4^{-2}~\Leftrightarrow~\dfrac{1}{4^2}~\Leftrightarrow~ \dfrac{1}{16} ~~~~\checkmark}\end{array}\)
\(\large\textsf{Choose all answers that are correct:}\\\\\mathsf{A)~~\checkmark}\\\mathsf{B)~~\checkmark}\\\mathsf{D)~~\checkmark}\\\mathsf{E)~~\checkmark}\\\mathsf{H)~~\checkmark}\\\mathsf{I)~~\checkmark}\\\mathsf{J)~~\checkmark}\)
