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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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