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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(q^{1}\right)^{\frac{1}{3}}\\= q^{ 1 . \frac{1}{3} }= q^{\frac{1}{3}}\\=\sqrt[3]{ q }\\---------------\)
2. \(\left(q^{\frac{2}{3}}\right)^{\frac{1}{6}}\\= q^{ \frac{2}{3} . \frac{1}{6} }= q^{\frac{1}{9}}\\=\sqrt[9]{ q }\\---------------\)
3. \(\left(a^{\frac{-1}{5}}\right)^{\frac{4}{5}}\\= a^{ \frac{-1}{5} . \frac{4}{5} }= a^{\frac{-4}{25}}\\=\frac{1}{\sqrt[25]{ a^{4} }}=\frac{1}{\sqrt[25]{ a^{4} }}. \color{purple}{\frac{\sqrt[25]{ a^{21} }}{\sqrt[25]{ a^{21} }}} \\=\frac{\sqrt[25]{ a^{21} }}{a}\\---------------\)
4. \(\left(a^{\frac{5}{4}}\right)^{1}\\= a^{ \frac{5}{4} . 1 }= a^{\frac{5}{4}}\\=\sqrt[4]{ a^{5} }=|a|.\sqrt[4]{ a }\\---------------\)
5. \(\left(a^{\frac{1}{5}}\right)^{-1}\\= a^{ \frac{1}{5} . (-1) }= a^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ a }}=\frac{1}{\sqrt[5]{ a }}. \color{purple}{\frac{\sqrt[5]{ a^{4} }}{\sqrt[5]{ a^{4} }}} \\=\frac{\sqrt[5]{ a^{4} }}{a}\\---------------\)
6. \(\left(y^{1}\right)^{\frac{-5}{3}}\\= y^{ 1 . (\frac{-5}{3}) }= y^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ y^{5} }}\\=\frac{1}{y.\sqrt[3]{ y^{2} }}=\frac{1}{y.\sqrt[3]{ y^{2} }} \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y^{2}}\\---------------\)
7. \(\left(q^{1}\right)^{\frac{3}{5}}\\= q^{ 1 . \frac{3}{5} }= q^{\frac{3}{5}}\\=\sqrt[5]{ q^{3} }\\---------------\)
8. \(\left(q^{\frac{5}{4}}\right)^{-1}\\= q^{ \frac{5}{4} . (-1) }= q^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ q^{5} }}\\=\frac{1}{|q|.\sqrt[4]{ q }}=\frac{1}{|q|.\sqrt[4]{ q }} \color{purple}{\frac{\sqrt[4]{ q^{3} }}{\sqrt[4]{ q^{3} }}} \\=\frac{\sqrt[4]{ q^{3} }}{|q^{2}|}\\---------------\)
9. \(\left(x^{\frac{2}{5}}\right)^{\frac{-5}{2}}\\= x^{ \frac{2}{5} . (\frac{-5}{2}) }= x^{-1}\\=\frac{1}{x}\\---------------\)
10. \(\left(q^{\frac{-4}{5}}\right)^{-1}\\= q^{ \frac{-4}{5} . (-1) }= q^{\frac{4}{5}}\\=\sqrt[5]{ q^{4} }\\---------------\)
11. \(\left(q^{-1}\right)^{\frac{5}{4}}\\= q^{ -1 . \frac{5}{4} }= q^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ q^{5} }}\\=\frac{1}{|q|.\sqrt[4]{ q }}=\frac{1}{|q|.\sqrt[4]{ q }} \color{purple}{\frac{\sqrt[4]{ q^{3} }}{\sqrt[4]{ q^{3} }}} \\=\frac{\sqrt[4]{ q^{3} }}{|q^{2}|}\\---------------\)
12. \(\left(y^{\frac{-4}{5}}\right)^{2}\\= y^{ \frac{-4}{5} . 2 }= y^{\frac{-8}{5}}\\=\frac{1}{\sqrt[5]{ y^{8} }}\\=\frac{1}{y.\sqrt[5]{ y^{3} }}=\frac{1}{y.\sqrt[5]{ y^{3} }} \color{purple}{\frac{\sqrt[5]{ y^{2} }}{\sqrt[5]{ y^{2} }}} \\=\frac{\sqrt[5]{ y^{2} }}{y^{2}}\\---------------\)