[tex](\frac{8}{27})^{\frac{-2}{3}}[/tex]
= [tex](\frac{27}{8})^{\frac{2}{3}[/tex]
= [tex]\sqrt[3]{(\frac{27}{8})^{2}}[/tex]
= [tex]\sqrt[3]{(\frac{27*27}{8*8})}[/tex]
= [tex]\frac{3*3}{2*2}[/tex]
= [tex]\frac{9}{4}[/tex]
Error: Student did not use the negative sign properly
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[tex](x^{-6}y^{6})(x^{\frac{-1}{6}}y^{5})[/tex]
= [tex]x^{-6}*x^{\frac{-1}{6}}*y^{6}*y^{5}[/tex]
= [tex]x^{-6-{\frac{1}{6}}}*y^{6+5}[/tex]
= [tex]x^{{\frac{-37}{6}}}y^{11}[/tex]
= [tex]\frac{y^{11}}{x^{\frac{37}{6}}}[/tex]
Error: Student multiplied the exponents instead of adding them
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[tex](\frac{2m^{\frac{1}{4}}}{n^{4}})^{-4}[/tex]
= [tex]\frac{2^{-4}m^{-1}}{n^{-16}}[/tex]
= [tex]\frac{n^{16}}{{2^{4}m^{1}}}[/tex]
= [tex]\frac{n^{16}}{{16m}}[/tex]
Error: Student did not distribute the exponent properly AND did not use the negative sign properly
