Werk uit m.b.v. de rekenregels
- \(\left(x^{\frac{5}{3}}\right)^{\frac{-3}{5}}\)
- \(\left(a^{\frac{1}{3}}\right)^{-2}\)
- \(\left(q^{\frac{-5}{3}}\right)^{\frac{5}{6}}\)
- \(\left(y^{\frac{3}{5}}\right)^{-1}\)
- \(\left(a^{\frac{-1}{3}}\right)^{\frac{-5}{2}}\)
- \(\left(x^{1}\right)^{\frac{3}{5}}\)
- \(\left(a^{\frac{1}{3}}\right)^{\frac{-1}{3}}\)
- \(\left(x^{\frac{-2}{5}}\right)^{-1}\)
- \(\left(q^{\frac{-3}{4}}\right)^{\frac{1}{3}}\)
- \(\left(q^{\frac{1}{2}}\right)^{\frac{3}{5}}\)
- \(\left(q^{\frac{-1}{3}}\right)^{-1}\)
- \(\left(y^{\frac{-5}{4}}\right)^{\frac{1}{2}}\)
Werk uit m.b.v. de rekenregels
Verbetersleutel
- \(\left(x^{\frac{5}{3}}\right)^{\frac{-3}{5}}\\= x^{ \frac{5}{3} . (\frac{-3}{5}) }= x^{-1}\\=\frac{1}{x}\\---------------\)
- \(\left(a^{\frac{1}{3}}\right)^{-2}\\= a^{ \frac{1}{3} . (-2) }= a^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ a^{2} }}=\frac{1}{\sqrt[3]{ a^{2} }}.
\color{purple}{\frac{\sqrt[3]{ a }}{\sqrt[3]{ a }}} \\=\frac{\sqrt[3]{ a }}{a}\\---------------\)
- \(\left(q^{\frac{-5}{3}}\right)^{\frac{5}{6}}\\= q^{ \frac{-5}{3} . \frac{5}{6} }= q^{\frac{-25}{18}}\\=\frac{1}{\sqrt[18]{ q^{25} }}\\=\frac{1}{|q|.\sqrt[18]{ q^{7} }}=\frac{1}{|q|.\sqrt[18]{ q^{7} }}
\color{purple}{\frac{\sqrt[18]{ q^{11} }}{\sqrt[18]{ q^{11} }}} \\=\frac{\sqrt[18]{ q^{11} }}{|q^{2}|}\\---------------\)
- \(\left(y^{\frac{3}{5}}\right)^{-1}\\= y^{ \frac{3}{5} . (-1) }= y^{\frac{-3}{5}}\\=\frac{1}{\sqrt[5]{ y^{3} }}=\frac{1}{\sqrt[5]{ y^{3} }}.
\color{purple}{\frac{\sqrt[5]{ y^{2} }}{\sqrt[5]{ y^{2} }}} \\=\frac{\sqrt[5]{ y^{2} }}{y}\\---------------\)
- \(\left(a^{\frac{-1}{3}}\right)^{\frac{-5}{2}}\\= a^{ \frac{-1}{3} . (\frac{-5}{2}) }= a^{\frac{5}{6}}\\=\sqrt[6]{ a^{5} }\\---------------\)
- \(\left(x^{1}\right)^{\frac{3}{5}}\\= x^{ 1 . \frac{3}{5} }= x^{\frac{3}{5}}\\=\sqrt[5]{ x^{3} }\\---------------\)
- \(\left(a^{\frac{1}{3}}\right)^{\frac{-1}{3}}\\= a^{ \frac{1}{3} . (\frac{-1}{3}) }= a^{\frac{-1}{9}}\\=\frac{1}{\sqrt[9]{ a }}=\frac{1}{\sqrt[9]{ a }}.
\color{purple}{\frac{\sqrt[9]{ a^{8} }}{\sqrt[9]{ a^{8} }}} \\=\frac{\sqrt[9]{ a^{8} }}{a}\\---------------\)
- \(\left(x^{\frac{-2}{5}}\right)^{-1}\\= x^{ \frac{-2}{5} . (-1) }= x^{\frac{2}{5}}\\=\sqrt[5]{ x^{2} }\\---------------\)
- \(\left(q^{\frac{-3}{4}}\right)^{\frac{1}{3}}\\= q^{ \frac{-3}{4} . \frac{1}{3} }= q^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ q }}=\frac{1}{\sqrt[4]{ q }}.
\color{purple}{\frac{\sqrt[4]{ q^{3} }}{\sqrt[4]{ q^{3} }}} \\=\frac{\sqrt[4]{ q^{3} }}{|q|}\\---------------\)
- \(\left(q^{\frac{1}{2}}\right)^{\frac{3}{5}}\\= q^{ \frac{1}{2} . \frac{3}{5} }= q^{\frac{3}{10}}\\=\sqrt[10]{ q^{3} }\\---------------\)
- \(\left(q^{\frac{-1}{3}}\right)^{-1}\\= q^{ \frac{-1}{3} . (-1) }= q^{\frac{1}{3}}\\=\sqrt[3]{ q }\\---------------\)
- \(\left(y^{\frac{-5}{4}}\right)^{\frac{1}{2}}\\= y^{ \frac{-5}{4} . \frac{1}{2} }= y^{\frac{-5}{8}}\\=\frac{1}{\sqrt[8]{ y^{5} }}=\frac{1}{\sqrt[8]{ y^{5} }}.
\color{purple}{\frac{\sqrt[8]{ y^{3} }}{\sqrt[8]{ y^{3} }}} \\=\frac{\sqrt[8]{ y^{3} }}{|y|}\\---------------\)