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Werk uit m.b.v. de rekenregels

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

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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. \(\left(a^{\frac{-4}{3}}\right)^{\frac{4}{5}}\\= a^{ \frac{-4}{3} . \frac{4}{5} }= a^{\frac{-16}{15}}\\=\frac{1}{\sqrt[15]{ a^{16} }}\\=\frac{1}{a.\sqrt[15]{ a }}=\frac{1}{a.\sqrt[15]{ a }} \color{purple}{\frac{\sqrt[15]{ a^{14} }}{\sqrt[15]{ a^{14} }}} \\=\frac{\sqrt[15]{ a^{14} }}{a^{2}}\\---------------\)
3. \(\left(y^{-1}\right)^{\frac{1}{5}}\\= y^{ -1 . \frac{1}{5} }= y^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ y }}=\frac{1}{\sqrt[5]{ y }}. \color{purple}{\frac{\sqrt[5]{ y^{4} }}{\sqrt[5]{ y^{4} }}} \\=\frac{\sqrt[5]{ y^{4} }}{y}\\---------------\)
4. \(\left(x^{\frac{1}{5}}\right)^{\frac{1}{4}}\\= x^{ \frac{1}{5} . \frac{1}{4} }= x^{\frac{1}{20}}\\=\sqrt[20]{ x }\\---------------\)
5. \(\left(a^{\frac{-2}{3}}\right)^{\frac{-2}{5}}\\= a^{ \frac{-2}{3} . (\frac{-2}{5}) }= a^{\frac{4}{15}}\\=\sqrt[15]{ a^{4} }\\---------------\)
6. \(\left(a^{\frac{5}{3}}\right)^{\frac{1}{2}}\\= a^{ \frac{5}{3} . \frac{1}{2} }= a^{\frac{5}{6}}\\=\sqrt[6]{ a^{5} }\\---------------\)
7. \(\left(y^{\frac{1}{4}}\right)^{1}\\= y^{ \frac{1}{4} . 1 }= y^{\frac{1}{4}}\\=\sqrt[4]{ y }\\---------------\)
8. \(\left(q^{\frac{-1}{3}}\right)^{\frac{1}{3}}\\= q^{ \frac{-1}{3} . \frac{1}{3} }= q^{\frac{-1}{9}}\\=\frac{1}{\sqrt[9]{ q }}=\frac{1}{\sqrt[9]{ q }}. \color{purple}{\frac{\sqrt[9]{ q^{8} }}{\sqrt[9]{ q^{8} }}} \\=\frac{\sqrt[9]{ q^{8} }}{q}\\---------------\)
9. \(\left(x^{\frac{-5}{6}}\right)^{-1}\\= x^{ \frac{-5}{6} . (-1) }= x^{\frac{5}{6}}\\=\sqrt[6]{ x^{5} }\\---------------\)
10. \(\left(x^{\frac{1}{5}}\right)^{\frac{-2}{5}}\\= x^{ \frac{1}{5} . (\frac{-2}{5}) }= x^{\frac{-2}{25}}\\=\frac{1}{\sqrt[25]{ x^{2} }}=\frac{1}{\sqrt[25]{ x^{2} }}. \color{purple}{\frac{\sqrt[25]{ x^{23} }}{\sqrt[25]{ x^{23} }}} \\=\frac{\sqrt[25]{ x^{23} }}{x}\\---------------\)
11. \(\left(q^{\frac{2}{3}}\right)^{\frac{1}{4}}\\= q^{ \frac{2}{3} . \frac{1}{4} }= q^{\frac{1}{6}}\\=\sqrt[6]{ q }\\---------------\)
12. \(\left(q^{\frac{-1}{5}}\right)^{\frac{-2}{5}}\\= q^{ \frac{-1}{5} . (\frac{-2}{5}) }= q^{\frac{2}{25}}\\=\sqrt[25]{ q^{2} }\\---------------\)