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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(y^{1}\right)^{1}\\= y^{ 1 . 1 }= y^{1}\\\\---------------\)
2. \(\left(q^{\frac{-1}{6}}\right)^{\frac{-3}{5}}\\= q^{ \frac{-1}{6} . (\frac{-3}{5}) }= q^{\frac{1}{10}}\\=\sqrt[10]{ q }\\---------------\)
3. \(\left(a^{\frac{2}{3}}\right)^{\frac{-1}{2}}\\= a^{ \frac{2}{3} . (\frac{-1}{2}) }= a^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ a }}=\frac{1}{\sqrt[3]{ a }}. \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a}\\---------------\)
4. \(\left(a^{-1}\right)^{\frac{-4}{3}}\\= a^{ -1 . (\frac{-4}{3}) }= a^{\frac{4}{3}}\\=\sqrt[3]{ a^{4} }=a.\sqrt[3]{ a }\\---------------\)
5. \(\left(q^{\frac{1}{5}}\right)^{\frac{1}{2}}\\= q^{ \frac{1}{5} . \frac{1}{2} }= q^{\frac{1}{10}}\\=\sqrt[10]{ q }\\---------------\)
6. \(\left(y^{\frac{5}{3}}\right)^{\frac{-2}{3}}\\= y^{ \frac{5}{3} . (\frac{-2}{3}) }= y^{\frac{-10}{9}}\\=\frac{1}{\sqrt[9]{ y^{10} }}\\=\frac{1}{y.\sqrt[9]{ y }}=\frac{1}{y.\sqrt[9]{ y }} \color{purple}{\frac{\sqrt[9]{ y^{8} }}{\sqrt[9]{ y^{8} }}} \\=\frac{\sqrt[9]{ y^{8} }}{y^{2}}\\---------------\)
7. \(\left(a^{\frac{5}{3}}\right)^{-1}\\= a^{ \frac{5}{3} . (-1) }= a^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ a^{5} }}\\=\frac{1}{a.\sqrt[3]{ a^{2} }}=\frac{1}{a.\sqrt[3]{ a^{2} }} \color{purple}{\frac{\sqrt[3]{ a }}{\sqrt[3]{ a }}} \\=\frac{\sqrt[3]{ a }}{a^{2}}\\---------------\)
8. \(\left(a^{\frac{1}{6}}\right)^{\frac{-1}{3}}\\= a^{ \frac{1}{6} . (\frac{-1}{3}) }= a^{\frac{-1}{18}}\\=\frac{1}{\sqrt[18]{ a }}=\frac{1}{\sqrt[18]{ a }}. \color{purple}{\frac{\sqrt[18]{ a^{17} }}{\sqrt[18]{ a^{17} }}} \\=\frac{\sqrt[18]{ a^{17} }}{|a|}\\---------------\)
9. \(\left(q^{\frac{-5}{4}}\right)^{\frac{-5}{6}}\\= q^{ \frac{-5}{4} . (\frac{-5}{6}) }= q^{\frac{25}{24}}\\=\sqrt[24]{ q^{25} }=|q|.\sqrt[24]{ q }\\---------------\)
10. \(\left(q^{\frac{-1}{2}}\right)^{\frac{-1}{5}}\\= q^{ \frac{-1}{2} . (\frac{-1}{5}) }= q^{\frac{1}{10}}\\=\sqrt[10]{ q }\\---------------\)
11. \(\left(x^{\frac{4}{5}}\right)^{\frac{-1}{2}}\\= x^{ \frac{4}{5} . (\frac{-1}{2}) }= x^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ x^{2} }}=\frac{1}{\sqrt[5]{ x^{2} }}. \color{purple}{\frac{\sqrt[5]{ x^{3} }}{\sqrt[5]{ x^{3} }}} \\=\frac{\sqrt[5]{ x^{3} }}{x}\\---------------\)
12. \(\left(q^{\frac{-1}{4}}\right)^{\frac{-2}{5}}\\= q^{ \frac{-1}{4} . (\frac{-2}{5}) }= q^{\frac{1}{10}}\\=\sqrt[10]{ q }\\---------------\)