[tex]\huge\text{Hey there!}[/tex]
[tex]\large\textsf{Which expressions have a value of }\mathsf{\dfrac{16}{81}?\ }\large\textsf{Check ALL that APPLY. }[/tex]
[tex]\mathsf{(\dfrac{2}{3})^4}\\\\\mathsf{= \bf \dfrac{2}{3}\times\dfrac{2}{3}\times\dfrac{2}{3}\times \dfrac{2}{3}}\\\\\mathsf{= \bf \dfrac{2\times2\times2\times2}{3\times3\times3\times3}}\\\\\mathsf{2\times2\times2\times2}\\\mathsf{2\times2 = \bf 4}\\\mathsf{4\times4= \bf 16}\\\\\mathsf{\dfrac{\bf 16}{3\times3\times3\times3}}\\\\\mathsf{3\times3\times3\times3}\\\mathsf{3\times3 = 9}\\\mathef{9\times9 = \bf 81}\\\\\mathsf{\dfrac{16}{\bf 81}}\\\\\mathsf{= \bf \dfrac{16}{81}}[/tex]
[tex]\large\text{Option A. could POSSIBLY be your ANSWER}[/tex]
[tex]\mathsf{(\dfrac{16}{3})^4}\\\\\mathsf{= \dfrac{16}{3}\times\dfrac{16}{3}\times\dfrac{16}{3}\times\dfrac{16}{3}}\\\\\mathsf{= \dfrac{16\times16\times16\times16}{3\times3\times3\times3}}\\\\\mathsf{16\times16\times16\times16}\\\mathsf{16\times16= \bf 256}\\\mathsf{256\times256 = \bf 65,536}\\\\\mathsf{\dfrac{\bf 65,536}{3\times3\times3\times3}}\\\\\mathsf{3\times3\times3\times3}\\\mathsf{3\times3 = \bf 9}\\\mathsf{9\times9 = \bf 81}\\\\\\\mathsf{\dfrac{65,536}{\bf 81}}\\\\\mathsf{\bf = \dfrac{65,536}{81}}[/tex]
[tex]\large\text{Option B. CANNOT be your POSSIBLE ANSWER}[/tex]
[tex]\mathsf{(\dfrac{4}{81})^2}\\\\\mathsf{=\dfrac{4}{81}\times\dfrac{4}{81}}\\\\\mathsf{= \dfrac{4\times4}{81\times81}}\\\\\mathsf{4\times4= \bf 16}\\\\\mathsf{\dfrac{\bf 16}{81\times81}}\\\\\mathsf{81\times81=\bf 6,561}\\\\\mathsf{\dfrac{16}{\bf 6,561}}\\\\\mathsf{= \bf \dfrac{16}{6,561}}[/tex]
[tex]\large\text{Option C. CANNOT be your POSSIBLE ANSWER}[/tex]
[tex]\mathsf{(\dfrac{4}{9})^2}\\\\\mathsf{= \dfrac{4}{9}\times \dfrac{4}{9}}\\\\\mathsf{= \dfrac{4\times4}{9\times9}}\\\\\mathsf{4\times4 = \bf 16}\\\\\mathsf{\dfrac{\bf 16}{9\times9}}\\\\\mathsf{9\times9 = \bf 81}\\\\\\\mathsf{\dfrac{16}{\bf 81}}\\\\\\\mathsf{= \bf \dfrac{16}{81}}[/tex]
[tex]\large\text{Option D. could POSSIBLY be your ANSWER}[/tex]
[tex]\mathsf{(\dfrac{1}{81})^1^6}\\\\\mathsf{= u n d e f i n e d\ (also\ known\ as\ 0)}[/tex]
[tex]\large\text{Option E. CANNOT be your POSSIBLE ANSWER}[/tex]
[tex]\boxed{\boxed{\mathsf{Answer:\bf Option\ A. (\dfrac{2}{3})^4} \&\ \bf Option\ D. (\dfrac{4}{9})^2}}}\huge\checkmark[/tex]
[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
