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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(q^{\frac{-3}{5}}\right)^{1}\\= q^{ \frac{-3}{5} . 1 }= q^{\frac{-3}{5}}\\=\frac{1}{\sqrt[5]{ q^{3} }}=\frac{1}{\sqrt[5]{ q^{3} }}. \color{purple}{\frac{\sqrt[5]{ q^{2} }}{\sqrt[5]{ q^{2} }}} \\=\frac{\sqrt[5]{ q^{2} }}{q}\\---------------\)
2. \(\left(q^{\frac{1}{2}}\right)^{\frac{-1}{6}}\\= q^{ \frac{1}{2} . (\frac{-1}{6}) }= q^{\frac{-1}{12}}\\=\frac{1}{\sqrt[12]{ q }}=\frac{1}{\sqrt[12]{ q }}. \color{purple}{\frac{\sqrt[12]{ q^{11} }}{\sqrt[12]{ q^{11} }}} \\=\frac{\sqrt[12]{ q^{11} }}{|q|}\\---------------\)
3. \(\left(a^{\frac{1}{6}}\right)^{\frac{-5}{3}}\\= a^{ \frac{1}{6} . (\frac{-5}{3}) }= a^{\frac{-5}{18}}\\=\frac{1}{\sqrt[18]{ a^{5} }}=\frac{1}{\sqrt[18]{ a^{5} }}. \color{purple}{\frac{\sqrt[18]{ a^{13} }}{\sqrt[18]{ a^{13} }}} \\=\frac{\sqrt[18]{ a^{13} }}{|a|}\\---------------\)
4. \(\left(y^{\frac{2}{3}}\right)^{\frac{-1}{2}}\\= y^{ \frac{2}{3} . (\frac{-1}{2}) }= y^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ y }}=\frac{1}{\sqrt[3]{ y }}. \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y}\\---------------\)
5. \(\left(x^{\frac{-2}{5}}\right)^{\frac{-2}{3}}\\= x^{ \frac{-2}{5} . (\frac{-2}{3}) }= x^{\frac{4}{15}}\\=\sqrt[15]{ x^{4} }\\---------------\)
6. \(\left(a^{\frac{-3}{4}}\right)^{\frac{2}{3}}\\= a^{ \frac{-3}{4} . \frac{2}{3} }= a^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ a } }=\frac{1}{ \sqrt{ a } }. \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a|}\\---------------\)
7. \(\left(q^{1}\right)^{-1}\\= q^{ 1 . (-1) }= q^{-1}\\=\frac{1}{q}\\---------------\)
8. \(\left(a^{1}\right)^{\frac{-4}{5}}\\= a^{ 1 . (\frac{-4}{5}) }= a^{\frac{-4}{5}}\\=\frac{1}{\sqrt[5]{ a^{4} }}=\frac{1}{\sqrt[5]{ a^{4} }}. \color{purple}{\frac{\sqrt[5]{ a }}{\sqrt[5]{ a }}} \\=\frac{\sqrt[5]{ a }}{a}\\---------------\)
9. \(\left(x^{\frac{-4}{3}}\right)^{\frac{1}{2}}\\= x^{ \frac{-4}{3} . \frac{1}{2} }= x^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ x^{2} }}=\frac{1}{\sqrt[3]{ x^{2} }}. \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x}\\---------------\)
10. \(\left(x^{\frac{-5}{2}}\right)^{\frac{-4}{3}}\\= x^{ \frac{-5}{2} . (\frac{-4}{3}) }= x^{\frac{10}{3}}\\=\sqrt[3]{ x^{10} }=x^{3}.\sqrt[3]{ x }\\---------------\)
11. \(\left(a^{\frac{-1}{4}}\right)^{\frac{-3}{4}}\\= a^{ \frac{-1}{4} . (\frac{-3}{4}) }= a^{\frac{3}{16}}\\=\sqrt[16]{ a^{3} }\\---------------\)
12. \(\left(q^{\frac{4}{5}}\right)^{1}\\= q^{ \frac{4}{5} . 1 }= q^{\frac{4}{5}}\\=\sqrt[5]{ q^{4} }\\---------------\)