Q:

Jayne evaluated an expression that has a value of 1/729. Which expression could Jayne have evaluated? Check all that apply.(-9)^39^-33^-6(1/9)^-6(1/3)^-6(-3)^6

Accepted Solution

A:
Answer:[tex](9)^{-3}[/tex][tex](3)^{-6}[/tex]Step-by-step explanation:we have[tex]\frac{1}{729}[/tex]Decompose the denominator in prime factors[tex]729=3^6[/tex]substitute[tex]\frac{1}{729}=\frac{1}{3^6}=3^{-6}[/tex]Verify each casecase 1) we have[tex](-9)^3=-729[/tex][tex]-729 \neq \frac{1}{729}[/tex]thereforeThis expression could not have been evaluated by Jaynecase 2) we have[tex](9)^{-3}=\frac{1}{9^{3}}=\frac{1}{729}[/tex][tex]\frac{1}{729}=\frac{1}{729}[/tex]thereforeThis expression could have been evaluated by Jaynecase 3) we have[tex](3)^{-6}=\frac{1}{3^{6}}=\frac{1}{729}[/tex][tex]\frac{1}{729}=\frac{1}{729}[/tex]thereforeThis expression could have been evaluated by Jaynecase 4) we have[tex](\frac{1}{9})^{-6}=9^{6}=531,441[/tex][tex]531,441 \neq \frac{1}{729}[/tex]thereforeThis expression could not have been evaluated by Jaynecase 5) we have[tex](\frac{1}{3})^{-6}=3^{6}=729[/tex][tex]729 \neq \frac{1}{729}[/tex]thereforeThis expression could not have been evaluated by Jaynecase 6) we have[tex](-3)^6=729[/tex][tex]729 \neq \frac{1}{729}[/tex]thereforeThis expression could not have been evaluated by Jayne