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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(a^{\frac{5}{6}}\right)^{\frac{5}{4}}\\= a^{ \frac{5}{6} . \frac{5}{4} }= a^{\frac{25}{24}}\\=\sqrt[24]{ a^{25} }=|a|.\sqrt[24]{ a }\\---------------\)
2. \(\left(y^{\frac{-4}{3}}\right)^{\frac{1}{3}}\\= y^{ \frac{-4}{3} . \frac{1}{3} }= y^{\frac{-4}{9}}\\=\frac{1}{\sqrt[9]{ y^{4} }}=\frac{1}{\sqrt[9]{ y^{4} }}. \color{purple}{\frac{\sqrt[9]{ y^{5} }}{\sqrt[9]{ y^{5} }}} \\=\frac{\sqrt[9]{ y^{5} }}{y}\\---------------\)
3. \(\left(y^{\frac{-2}{3}}\right)^{1}\\= y^{ \frac{-2}{3} . 1 }= y^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ y^{2} }}=\frac{1}{\sqrt[3]{ y^{2} }}. \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y}\\---------------\)
4. \(\left(y^{\frac{3}{2}}\right)^{\frac{-5}{4}}\\= y^{ \frac{3}{2} . (\frac{-5}{4}) }= y^{\frac{-15}{8}}\\=\frac{1}{\sqrt[8]{ y^{15} }}\\=\frac{1}{|y|.\sqrt[8]{ y^{7} }}=\frac{1}{|y|.\sqrt[8]{ y^{7} }} \color{purple}{\frac{\sqrt[8]{ y }}{\sqrt[8]{ y }}} \\=\frac{\sqrt[8]{ y }}{|y^{2}|}\\---------------\)
5. \(\left(q^{\frac{5}{3}}\right)^{\frac{-1}{3}}\\= q^{ \frac{5}{3} . (\frac{-1}{3}) }= q^{\frac{-5}{9}}\\=\frac{1}{\sqrt[9]{ q^{5} }}=\frac{1}{\sqrt[9]{ q^{5} }}. \color{purple}{\frac{\sqrt[9]{ q^{4} }}{\sqrt[9]{ q^{4} }}} \\=\frac{\sqrt[9]{ q^{4} }}{q}\\---------------\)
6. \(\left(y^{-1}\right)^{\frac{-1}{2}}\\= y^{ -1 . (\frac{-1}{2}) }= y^{\frac{1}{2}}\\= \sqrt{ y } \\---------------\)
7. \(\left(q^{\frac{1}{2}}\right)^{\frac{-5}{4}}\\= q^{ \frac{1}{2} . (\frac{-5}{4}) }= q^{\frac{-5}{8}}\\=\frac{1}{\sqrt[8]{ q^{5} }}=\frac{1}{\sqrt[8]{ q^{5} }}. \color{purple}{\frac{\sqrt[8]{ q^{3} }}{\sqrt[8]{ q^{3} }}} \\=\frac{\sqrt[8]{ q^{3} }}{|q|}\\---------------\)
8. \(\left(q^{\frac{2}{3}}\right)^{1}\\= q^{ \frac{2}{3} . 1 }= q^{\frac{2}{3}}\\=\sqrt[3]{ q^{2} }\\---------------\)
9. \(\left(a^{\frac{-1}{2}}\right)^{\frac{5}{4}}\\= a^{ \frac{-1}{2} . \frac{5}{4} }= a^{\frac{-5}{8}}\\=\frac{1}{\sqrt[8]{ a^{5} }}=\frac{1}{\sqrt[8]{ a^{5} }}. \color{purple}{\frac{\sqrt[8]{ a^{3} }}{\sqrt[8]{ a^{3} }}} \\=\frac{\sqrt[8]{ a^{3} }}{|a|}\\---------------\)
10. \(\left(q^{1}\right)^{\frac{1}{3}}\\= q^{ 1 . \frac{1}{3} }= q^{\frac{1}{3}}\\=\sqrt[3]{ q }\\---------------\)
11. \(\left(y^{\frac{4}{5}}\right)^{\frac{1}{2}}\\= y^{ \frac{4}{5} . \frac{1}{2} }= y^{\frac{2}{5}}\\=\sqrt[5]{ y^{2} }\\---------------\)
12. \(\left(x^{\frac{-2}{5}}\right)^{-1}\\= x^{ \frac{-2}{5} . (-1) }= x^{\frac{2}{5}}\\=\sqrt[5]{ x^{2} }\\---------------\)