Werk uit m.b.v. de rekenregels
- \(\left(y^{\frac{5}{6}}\right)^{-1}\)
- \(\left(y^{\frac{1}{3}}\right)^{\frac{2}{3}}\)
- \(\left(q^{\frac{1}{3}}\right)^{\frac{-1}{3}}\)
- \(\left(q^{\frac{-2}{3}}\right)^{1}\)
- \(\left(q^{\frac{-1}{3}}\right)^{\frac{-1}{3}}\)
- \(\left(a^{\frac{5}{6}}\right)^{\frac{1}{4}}\)
- \(\left(x^{\frac{2}{3}}\right)^{\frac{3}{2}}\)
- \(\left(a^{\frac{-4}{3}}\right)^{\frac{2}{3}}\)
- \(\left(q^{\frac{1}{4}}\right)^{\frac{-1}{3}}\)
- \(\left(x^{\frac{2}{3}}\right)^{\frac{-5}{4}}\)
- \(\left(y^{-1}\right)^{\frac{-2}{5}}\)
- \(\left(y^{\frac{3}{2}}\right)^{\frac{-1}{6}}\)
Werk uit m.b.v. de rekenregels
Verbetersleutel
- \(\left(y^{\frac{5}{6}}\right)^{-1}\\= y^{ \frac{5}{6} . (-1) }= y^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ y^{5} }}=\frac{1}{\sqrt[6]{ y^{5} }}.
\color{purple}{\frac{\sqrt[6]{ y }}{\sqrt[6]{ y }}} \\=\frac{\sqrt[6]{ y }}{|y|}\\---------------\)
- \(\left(y^{\frac{1}{3}}\right)^{\frac{2}{3}}\\= y^{ \frac{1}{3} . \frac{2}{3} }= y^{\frac{2}{9}}\\=\sqrt[9]{ y^{2} }\\---------------\)
- \(\left(q^{\frac{1}{3}}\right)^{\frac{-1}{3}}\\= q^{ \frac{1}{3} . (\frac{-1}{3}) }= q^{\frac{-1}{9}}\\=\frac{1}{\sqrt[9]{ q }}=\frac{1}{\sqrt[9]{ q }}.
\color{purple}{\frac{\sqrt[9]{ q^{8} }}{\sqrt[9]{ q^{8} }}} \\=\frac{\sqrt[9]{ q^{8} }}{q}\\---------------\)
- \(\left(q^{\frac{-2}{3}}\right)^{1}\\= q^{ \frac{-2}{3} . 1 }= q^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ q^{2} }}=\frac{1}{\sqrt[3]{ q^{2} }}.
\color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q}\\---------------\)
- \(\left(q^{\frac{-1}{3}}\right)^{\frac{-1}{3}}\\= q^{ \frac{-1}{3} . (\frac{-1}{3}) }= q^{\frac{1}{9}}\\=\sqrt[9]{ q }\\---------------\)
- \(\left(a^{\frac{5}{6}}\right)^{\frac{1}{4}}\\= a^{ \frac{5}{6} . \frac{1}{4} }= a^{\frac{5}{24}}\\=\sqrt[24]{ a^{5} }\\---------------\)
- \(\left(x^{\frac{2}{3}}\right)^{\frac{3}{2}}\\= x^{ \frac{2}{3} . \frac{3}{2} }= x^{1}\\\\---------------\)
- \(\left(a^{\frac{-4}{3}}\right)^{\frac{2}{3}}\\= a^{ \frac{-4}{3} . \frac{2}{3} }= a^{\frac{-8}{9}}\\=\frac{1}{\sqrt[9]{ a^{8} }}=\frac{1}{\sqrt[9]{ a^{8} }}.
\color{purple}{\frac{\sqrt[9]{ a }}{\sqrt[9]{ a }}} \\=\frac{\sqrt[9]{ a }}{a}\\---------------\)
- \(\left(q^{\frac{1}{4}}\right)^{\frac{-1}{3}}\\= q^{ \frac{1}{4} . (\frac{-1}{3}) }= q^{\frac{-1}{12}}\\=\frac{1}{\sqrt[12]{ q }}=\frac{1}{\sqrt[12]{ q }}.
\color{purple}{\frac{\sqrt[12]{ q^{11} }}{\sqrt[12]{ q^{11} }}} \\=\frac{\sqrt[12]{ q^{11} }}{|q|}\\---------------\)
- \(\left(x^{\frac{2}{3}}\right)^{\frac{-5}{4}}\\= x^{ \frac{2}{3} . (\frac{-5}{4}) }= x^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ x^{5} }}=\frac{1}{\sqrt[6]{ x^{5} }}.
\color{purple}{\frac{\sqrt[6]{ x }}{\sqrt[6]{ x }}} \\=\frac{\sqrt[6]{ x }}{|x|}\\---------------\)
- \(\left(y^{-1}\right)^{\frac{-2}{5}}\\= y^{ -1 . (\frac{-2}{5}) }= y^{\frac{2}{5}}\\=\sqrt[5]{ y^{2} }\\---------------\)
- \(\left(y^{\frac{3}{2}}\right)^{\frac{-1}{6}}\\= y^{ \frac{3}{2} . (\frac{-1}{6}) }= y^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ y }}=\frac{1}{\sqrt[4]{ y }}.
\color{purple}{\frac{\sqrt[4]{ y^{3} }}{\sqrt[4]{ y^{3} }}} \\=\frac{\sqrt[4]{ y^{3} }}{|y|}\\---------------\)