Werk uit m.b.v. de rekenregels
- \(\left(a^{\frac{1}{2}}\right)^{\frac{-1}{6}}\)
- \(\left(q^{-1}\right)^{\frac{1}{4}}\)
- \(\left(x^{1}\right)^{\frac{2}{3}}\)
- \(\left(a^{-1}\right)^{\frac{-3}{5}}\)
- \(\left(a^{1}\right)^{\frac{-1}{6}}\)
- \(\left(q^{\frac{1}{6}}\right)^{\frac{4}{5}}\)
- \(\left(a^{\frac{-5}{6}}\right)^{\frac{-3}{4}}\)
- \(\left(q^{\frac{-1}{2}}\right)^{-1}\)
- \(\left(q^{\frac{-5}{4}}\right)^{\frac{-5}{2}}\)
- \(\left(a^{\frac{-1}{4}}\right)^{1}\)
- \(\left(q^{1}\right)^{\frac{5}{4}}\)
- \(\left(a^{\frac{-1}{3}}\right)^{\frac{-1}{3}}\)
Werk uit m.b.v. de rekenregels
Verbetersleutel
- \(\left(a^{\frac{1}{2}}\right)^{\frac{-1}{6}}\\= a^{ \frac{1}{2} . (\frac{-1}{6}) }= a^{\frac{-1}{12}}\\=\frac{1}{\sqrt[12]{ a }}=\frac{1}{\sqrt[12]{ a }}.
\color{purple}{\frac{\sqrt[12]{ a^{11} }}{\sqrt[12]{ a^{11} }}} \\=\frac{\sqrt[12]{ a^{11} }}{|a|}\\---------------\)
- \(\left(q^{-1}\right)^{\frac{1}{4}}\\= q^{ -1 . \frac{1}{4} }= q^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ q }}=\frac{1}{\sqrt[4]{ q }}.
\color{purple}{\frac{\sqrt[4]{ q^{3} }}{\sqrt[4]{ q^{3} }}} \\=\frac{\sqrt[4]{ q^{3} }}{|q|}\\---------------\)
- \(\left(x^{1}\right)^{\frac{2}{3}}\\= x^{ 1 . \frac{2}{3} }= x^{\frac{2}{3}}\\=\sqrt[3]{ x^{2} }\\---------------\)
- \(\left(a^{-1}\right)^{\frac{-3}{5}}\\= a^{ -1 . (\frac{-3}{5}) }= a^{\frac{3}{5}}\\=\sqrt[5]{ a^{3} }\\---------------\)
- \(\left(a^{1}\right)^{\frac{-1}{6}}\\= a^{ 1 . (\frac{-1}{6}) }= a^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ a }}=\frac{1}{\sqrt[6]{ a }}.
\color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a|}\\---------------\)
- \(\left(q^{\frac{1}{6}}\right)^{\frac{4}{5}}\\= q^{ \frac{1}{6} . \frac{4}{5} }= q^{\frac{2}{15}}\\=\sqrt[15]{ q^{2} }\\---------------\)
- \(\left(a^{\frac{-5}{6}}\right)^{\frac{-3}{4}}\\= a^{ \frac{-5}{6} . (\frac{-3}{4}) }= a^{\frac{5}{8}}\\=\sqrt[8]{ a^{5} }\\---------------\)
- \(\left(q^{\frac{-1}{2}}\right)^{-1}\\= q^{ \frac{-1}{2} . (-1) }= q^{\frac{1}{2}}\\= \sqrt{ q } \\---------------\)
- \(\left(q^{\frac{-5}{4}}\right)^{\frac{-5}{2}}\\= q^{ \frac{-5}{4} . (\frac{-5}{2}) }= q^{\frac{25}{8}}\\=\sqrt[8]{ q^{25} }=|q^{3}|.\sqrt[8]{ q }\\---------------\)
- \(\left(a^{\frac{-1}{4}}\right)^{1}\\= a^{ \frac{-1}{4} . 1 }= a^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ a }}=\frac{1}{\sqrt[4]{ a }}.
\color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a|}\\---------------\)
- \(\left(q^{1}\right)^{\frac{5}{4}}\\= q^{ 1 . \frac{5}{4} }= q^{\frac{5}{4}}\\=\sqrt[4]{ q^{5} }=|q|.\sqrt[4]{ q }\\---------------\)
- \(\left(a^{\frac{-1}{3}}\right)^{\frac{-1}{3}}\\= a^{ \frac{-1}{3} . (\frac{-1}{3}) }= a^{\frac{1}{9}}\\=\sqrt[9]{ a }\\---------------\)