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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{\frac{-3}{4}}\right)^{-1}\\= x^{ \frac{-3}{4} . (-1) }= x^{\frac{3}{4}}\\=\sqrt[4]{ x^{3} }\\---------------\)
2. \(\left(y^{-1}\right)^{-1}\\= y^{ -1 . (-1) }= y^{1}\\\\---------------\)
3. \(\left(x^{\frac{2}{3}}\right)^{\frac{1}{6}}\\= x^{ \frac{2}{3} . \frac{1}{6} }= x^{\frac{1}{9}}\\=\sqrt[9]{ x }\\---------------\)
4. \(\left(a^{\frac{1}{4}}\right)^{\frac{1}{5}}\\= a^{ \frac{1}{4} . \frac{1}{5} }= a^{\frac{1}{20}}\\=\sqrt[20]{ a }\\---------------\)
5. \(\left(x^{-1}\right)^{\frac{-1}{4}}\\= x^{ -1 . (\frac{-1}{4}) }= x^{\frac{1}{4}}\\=\sqrt[4]{ x }\\---------------\)
6. \(\left(a^{\frac{1}{3}}\right)^{-1}\\= a^{ \frac{1}{3} . (-1) }= a^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ a }}=\frac{1}{\sqrt[3]{ a }}. \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a}\\---------------\)
7. \(\left(a^{1}\right)^{\frac{-2}{3}}\\= a^{ 1 . (\frac{-2}{3}) }= a^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ a^{2} }}=\frac{1}{\sqrt[3]{ a^{2} }}. \color{purple}{\frac{\sqrt[3]{ a }}{\sqrt[3]{ a }}} \\=\frac{\sqrt[3]{ a }}{a}\\---------------\)
8. \(\left(x^{\frac{5}{4}}\right)^{\frac{-1}{3}}\\= x^{ \frac{5}{4} . (\frac{-1}{3}) }= x^{\frac{-5}{12}}\\=\frac{1}{\sqrt[12]{ x^{5} }}=\frac{1}{\sqrt[12]{ x^{5} }}. \color{purple}{\frac{\sqrt[12]{ x^{7} }}{\sqrt[12]{ x^{7} }}} \\=\frac{\sqrt[12]{ x^{7} }}{|x|}\\---------------\)
9. \(\left(q^{-1}\right)^{\frac{-1}{3}}\\= q^{ -1 . (\frac{-1}{3}) }= q^{\frac{1}{3}}\\=\sqrt[3]{ q }\\---------------\)
10. \(\left(y^{\frac{-2}{5}}\right)^{\frac{2}{5}}\\= y^{ \frac{-2}{5} . \frac{2}{5} }= y^{\frac{-4}{25}}\\=\frac{1}{\sqrt[25]{ y^{4} }}=\frac{1}{\sqrt[25]{ y^{4} }}. \color{purple}{\frac{\sqrt[25]{ y^{21} }}{\sqrt[25]{ y^{21} }}} \\=\frac{\sqrt[25]{ y^{21} }}{y}\\---------------\)
11. \(\left(q^{\frac{2}{3}}\right)^{\frac{-1}{5}}\\= q^{ \frac{2}{3} . (\frac{-1}{5}) }= q^{\frac{-2}{15}}\\=\frac{1}{\sqrt[15]{ q^{2} }}=\frac{1}{\sqrt[15]{ q^{2} }}. \color{purple}{\frac{\sqrt[15]{ q^{13} }}{\sqrt[15]{ q^{13} }}} \\=\frac{\sqrt[15]{ q^{13} }}{q}\\---------------\)
12. \(\left(y^{\frac{1}{3}}\right)^{\frac{1}{4}}\\= y^{ \frac{1}{3} . \frac{1}{4} }= y^{\frac{1}{12}}\\=\sqrt[12]{ y }\\---------------\)