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Werk uit m.b.v. de rekenregels

1. \(\left(x^{\frac{-2}{3}}\right)^{\frac{-2}{5}}\)
2. \(\left(q^{\frac{3}{4}}\right)^{\frac{-2}{3}}\)
3. \(\left(q^{\frac{3}{4}}\right)^{\frac{-1}{3}}\)
4. \(\left(y^{\frac{-1}{2}}\right)^{\frac{1}{2}}\)
5. \(\left(y^{\frac{2}{3}}\right)^{\frac{-5}{2}}\)
6. \(\left(a^{\frac{-5}{6}}\right)^{1}\)
7. \(\left(y^{1}\right)^{\frac{1}{2}}\)
8. \(\left(y^{\frac{1}{6}}\right)^{\frac{5}{4}}\)
9. \(\left(x^{\frac{-5}{6}}\right)^{\frac{-2}{3}}\)
10. \(\left(x^{\frac{1}{5}}\right)^{\frac{1}{4}}\)
11. \(\left(y^{\frac{4}{5}}\right)^{-1}\)
12. \(\left(q^{\frac{-1}{4}}\right)^{\frac{-1}{2}}\)

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{\frac{-2}{3}}\right)^{\frac{-2}{5}}\\= x^{ \frac{-2}{3} . (\frac{-2}{5}) }= x^{\frac{4}{15}}\\=\sqrt[15]{ x^{4} }\\---------------\)
2. \(\left(q^{\frac{3}{4}}\right)^{\frac{-2}{3}}\\= q^{ \frac{3}{4} . (\frac{-2}{3}) }= q^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ q } }=\frac{1}{ \sqrt{ q } }. \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q|}\\---------------\)
3. \(\left(q^{\frac{3}{4}}\right)^{\frac{-1}{3}}\\= q^{ \frac{3}{4} . (\frac{-1}{3}) }= q^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ q }}=\frac{1}{\sqrt[4]{ q }}. \color{purple}{\frac{\sqrt[4]{ q^{3} }}{\sqrt[4]{ q^{3} }}} \\=\frac{\sqrt[4]{ q^{3} }}{|q|}\\---------------\)
4. \(\left(y^{\frac{-1}{2}}\right)^{\frac{1}{2}}\\= y^{ \frac{-1}{2} . \frac{1}{2} }= y^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ y }}=\frac{1}{\sqrt[4]{ y }}. \color{purple}{\frac{\sqrt[4]{ y^{3} }}{\sqrt[4]{ y^{3} }}} \\=\frac{\sqrt[4]{ y^{3} }}{|y|}\\---------------\)
5. \(\left(y^{\frac{2}{3}}\right)^{\frac{-5}{2}}\\= y^{ \frac{2}{3} . (\frac{-5}{2}) }= y^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ y^{5} }}\\=\frac{1}{y.\sqrt[3]{ y^{2} }}=\frac{1}{y.\sqrt[3]{ y^{2} }} \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y^{2}}\\---------------\)
6. \(\left(a^{\frac{-5}{6}}\right)^{1}\\= a^{ \frac{-5}{6} . 1 }= a^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ a^{5} }}=\frac{1}{\sqrt[6]{ a^{5} }}. \color{purple}{\frac{\sqrt[6]{ a }}{\sqrt[6]{ a }}} \\=\frac{\sqrt[6]{ a }}{|a|}\\---------------\)
7. \(\left(y^{1}\right)^{\frac{1}{2}}\\= y^{ 1 . \frac{1}{2} }= y^{\frac{1}{2}}\\= \sqrt{ y } \\---------------\)
8. \(\left(y^{\frac{1}{6}}\right)^{\frac{5}{4}}\\= y^{ \frac{1}{6} . \frac{5}{4} }= y^{\frac{5}{24}}\\=\sqrt[24]{ y^{5} }\\---------------\)
9. \(\left(x^{\frac{-5}{6}}\right)^{\frac{-2}{3}}\\= x^{ \frac{-5}{6} . (\frac{-2}{3}) }= x^{\frac{5}{9}}\\=\sqrt[9]{ x^{5} }\\---------------\)
10. \(\left(x^{\frac{1}{5}}\right)^{\frac{1}{4}}\\= x^{ \frac{1}{5} . \frac{1}{4} }= x^{\frac{1}{20}}\\=\sqrt[20]{ x }\\---------------\)
11. \(\left(y^{\frac{4}{5}}\right)^{-1}\\= y^{ \frac{4}{5} . (-1) }= y^{\frac{-4}{5}}\\=\frac{1}{\sqrt[5]{ y^{4} }}=\frac{1}{\sqrt[5]{ y^{4} }}. \color{purple}{\frac{\sqrt[5]{ y }}{\sqrt[5]{ y }}} \\=\frac{\sqrt[5]{ y }}{y}\\---------------\)
12. \(\left(q^{\frac{-1}{4}}\right)^{\frac{-1}{2}}\\= q^{ \frac{-1}{4} . (\frac{-1}{2}) }= q^{\frac{1}{8}}\\=\sqrt[8]{ q }\\---------------\)