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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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