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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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