Werk uit m.b.v. de rekenregels
- \(\left(x^{\frac{-3}{5}}\right)^{\frac{5}{4}}\)
- \(\left(a^{\frac{2}{3}}\right)^{2}\)
- \(\left(a^{\frac{1}{6}}\right)^{\frac{1}{6}}\)
- \(\left(x^{\frac{4}{5}}\right)^{\frac{3}{5}}\)
- \(\left(q^{1}\right)^{\frac{2}{3}}\)
- \(\left(q^{\frac{1}{6}}\right)^{\frac{5}{6}}\)
- \(\left(q^{\frac{1}{2}}\right)^{\frac{1}{5}}\)
- \(\left(a^{-1}\right)^{\frac{3}{2}}\)
- \(\left(a^{2}\right)^{\frac{-3}{2}}\)
- \(\left(a^{\frac{4}{3}}\right)^{-1}\)
- \(\left(q^{\frac{3}{2}}\right)^{\frac{1}{2}}\)
- \(\left(y^{\frac{-5}{3}}\right)^{\frac{-1}{5}}\)
Werk uit m.b.v. de rekenregels
Verbetersleutel
- \(\left(x^{\frac{-3}{5}}\right)^{\frac{5}{4}}\\= x^{ \frac{-3}{5} . \frac{5}{4} }= x^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ x^{3} }}=\frac{1}{\sqrt[4]{ x^{3} }}.
\color{purple}{\frac{\sqrt[4]{ x }}{\sqrt[4]{ x }}} \\=\frac{\sqrt[4]{ x }}{|x|}\\---------------\)
- \(\left(a^{\frac{2}{3}}\right)^{2}\\= a^{ \frac{2}{3} . 2 }= a^{\frac{4}{3}}\\=\sqrt[3]{ a^{4} }=a.\sqrt[3]{ a }\\---------------\)
- \(\left(a^{\frac{1}{6}}\right)^{\frac{1}{6}}\\= a^{ \frac{1}{6} . \frac{1}{6} }= a^{\frac{1}{36}}\\=\sqrt[36]{ a }\\---------------\)
- \(\left(x^{\frac{4}{5}}\right)^{\frac{3}{5}}\\= x^{ \frac{4}{5} . \frac{3}{5} }= x^{\frac{12}{25}}\\=\sqrt[25]{ x^{12} }\\---------------\)
- \(\left(q^{1}\right)^{\frac{2}{3}}\\= q^{ 1 . \frac{2}{3} }= q^{\frac{2}{3}}\\=\sqrt[3]{ q^{2} }\\---------------\)
- \(\left(q^{\frac{1}{6}}\right)^{\frac{5}{6}}\\= q^{ \frac{1}{6} . \frac{5}{6} }= q^{\frac{5}{36}}\\=\sqrt[36]{ q^{5} }\\---------------\)
- \(\left(q^{\frac{1}{2}}\right)^{\frac{1}{5}}\\= q^{ \frac{1}{2} . \frac{1}{5} }= q^{\frac{1}{10}}\\=\sqrt[10]{ q }\\---------------\)
- \(\left(a^{-1}\right)^{\frac{3}{2}}\\= a^{ -1 . \frac{3}{2} }= a^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ a^{3} } }\\=\frac{1}{|a|. \sqrt{ a } }=\frac{1}{|a|. \sqrt{ a } }
\color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a^{2}|}\\---------------\)
- \(\left(a^{2}\right)^{\frac{-3}{2}}\\= a^{ 2 . (\frac{-3}{2}) }= a^{-3}\\=\frac{1}{a^{3}}\\---------------\)
- \(\left(a^{\frac{4}{3}}\right)^{-1}\\= a^{ \frac{4}{3} . (-1) }= a^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ a^{4} }}\\=\frac{1}{a.\sqrt[3]{ a }}=\frac{1}{a.\sqrt[3]{ a }}
\color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a^{2}}\\---------------\)
- \(\left(q^{\frac{3}{2}}\right)^{\frac{1}{2}}\\= q^{ \frac{3}{2} . \frac{1}{2} }= q^{\frac{3}{4}}\\=\sqrt[4]{ q^{3} }\\---------------\)
- \(\left(y^{\frac{-5}{3}}\right)^{\frac{-1}{5}}\\= y^{ \frac{-5}{3} . (\frac{-1}{5}) }= y^{\frac{1}{3}}\\=\sqrt[3]{ y }\\---------------\)