Werk uit m.b.v. de rekenregels
- \(\left(y^{\frac{1}{5}}\right)^{\frac{-5}{6}}\)
- \(\left(a^{\frac{1}{6}}\right)^{\frac{-3}{4}}\)
- \(\left(q^{\frac{1}{6}}\right)^{1}\)
- \(\left(a^{\frac{-4}{5}}\right)^{\frac{-1}{2}}\)
- \(\left(y^{\frac{-1}{3}}\right)^{-1}\)
- \(\left(y^{\frac{1}{4}}\right)^{-1}\)
- \(\left(x^{\frac{-2}{3}}\right)^{\frac{-3}{2}}\)
- \(\left(y^{\frac{-5}{2}}\right)^{\frac{-2}{3}}\)
- \(\left(a^{\frac{-1}{5}}\right)^{\frac{3}{4}}\)
- \(\left(y^{-1}\right)^{\frac{1}{2}}\)
- \(\left(y^{\frac{-5}{4}}\right)^{\frac{1}{6}}\)
- \(\left(y^{\frac{5}{4}}\right)^{\frac{-1}{2}}\)
Werk uit m.b.v. de rekenregels
Verbetersleutel
- \(\left(y^{\frac{1}{5}}\right)^{\frac{-5}{6}}\\= y^{ \frac{1}{5} . (\frac{-5}{6}) }= y^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ y }}=\frac{1}{\sqrt[6]{ y }}.
\color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y|}\\---------------\)
- \(\left(a^{\frac{1}{6}}\right)^{\frac{-3}{4}}\\= a^{ \frac{1}{6} . (\frac{-3}{4}) }= a^{\frac{-1}{8}}\\=\frac{1}{\sqrt[8]{ a }}=\frac{1}{\sqrt[8]{ a }}.
\color{purple}{\frac{\sqrt[8]{ a^{7} }}{\sqrt[8]{ a^{7} }}} \\=\frac{\sqrt[8]{ a^{7} }}{|a|}\\---------------\)
- \(\left(q^{\frac{1}{6}}\right)^{1}\\= q^{ \frac{1}{6} . 1 }= q^{\frac{1}{6}}\\=\sqrt[6]{ q }\\---------------\)
- \(\left(a^{\frac{-4}{5}}\right)^{\frac{-1}{2}}\\= a^{ \frac{-4}{5} . (\frac{-1}{2}) }= a^{\frac{2}{5}}\\=\sqrt[5]{ a^{2} }\\---------------\)
- \(\left(y^{\frac{-1}{3}}\right)^{-1}\\= y^{ \frac{-1}{3} . (-1) }= y^{\frac{1}{3}}\\=\sqrt[3]{ y }\\---------------\)
- \(\left(y^{\frac{1}{4}}\right)^{-1}\\= y^{ \frac{1}{4} . (-1) }= y^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ y }}=\frac{1}{\sqrt[4]{ y }}.
\color{purple}{\frac{\sqrt[4]{ y^{3} }}{\sqrt[4]{ y^{3} }}} \\=\frac{\sqrt[4]{ y^{3} }}{|y|}\\---------------\)
- \(\left(x^{\frac{-2}{3}}\right)^{\frac{-3}{2}}\\= x^{ \frac{-2}{3} . (\frac{-3}{2}) }= x^{1}\\\\---------------\)
- \(\left(y^{\frac{-5}{2}}\right)^{\frac{-2}{3}}\\= y^{ \frac{-5}{2} . (\frac{-2}{3}) }= y^{\frac{5}{3}}\\=\sqrt[3]{ y^{5} }=y.\sqrt[3]{ y^{2} }\\---------------\)
- \(\left(a^{\frac{-1}{5}}\right)^{\frac{3}{4}}\\= a^{ \frac{-1}{5} . \frac{3}{4} }= a^{\frac{-3}{20}}\\=\frac{1}{\sqrt[20]{ a^{3} }}=\frac{1}{\sqrt[20]{ a^{3} }}.
\color{purple}{\frac{\sqrt[20]{ a^{17} }}{\sqrt[20]{ a^{17} }}} \\=\frac{\sqrt[20]{ a^{17} }}{|a|}\\---------------\)
- \(\left(y^{-1}\right)^{\frac{1}{2}}\\= y^{ -1 . \frac{1}{2} }= y^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ y } }=\frac{1}{ \sqrt{ y } }.
\color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y|}\\---------------\)
- \(\left(y^{\frac{-5}{4}}\right)^{\frac{1}{6}}\\= y^{ \frac{-5}{4} . \frac{1}{6} }= y^{\frac{-5}{24}}\\=\frac{1}{\sqrt[24]{ y^{5} }}=\frac{1}{\sqrt[24]{ y^{5} }}.
\color{purple}{\frac{\sqrt[24]{ y^{19} }}{\sqrt[24]{ y^{19} }}} \\=\frac{\sqrt[24]{ y^{19} }}{|y|}\\---------------\)
- \(\left(y^{\frac{5}{4}}\right)^{\frac{-1}{2}}\\= y^{ \frac{5}{4} . (\frac{-1}{2}) }= y^{\frac{-5}{8}}\\=\frac{1}{\sqrt[8]{ y^{5} }}=\frac{1}{\sqrt[8]{ y^{5} }}.
\color{purple}{\frac{\sqrt[8]{ y^{3} }}{\sqrt[8]{ y^{3} }}} \\=\frac{\sqrt[8]{ y^{3} }}{|y|}\\---------------\)