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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(y^{\frac{-4}{3}}\right)^{\frac{-1}{4}}\\= y^{ \frac{-4}{3} . (\frac{-1}{4}) }= y^{\frac{1}{3}}\\=\sqrt[3]{ y }\\---------------\)
2. \(\left(a^{\frac{4}{5}}\right)^{\frac{-1}{6}}\\= a^{ \frac{4}{5} . (\frac{-1}{6}) }= a^{\frac{-2}{15}}\\=\frac{1}{\sqrt[15]{ a^{2} }}=\frac{1}{\sqrt[15]{ a^{2} }}. \color{purple}{\frac{\sqrt[15]{ a^{13} }}{\sqrt[15]{ a^{13} }}} \\=\frac{\sqrt[15]{ a^{13} }}{a}\\---------------\)
3. \(\left(a^{\frac{-1}{3}}\right)^{\frac{-1}{2}}\\= a^{ \frac{-1}{3} . (\frac{-1}{2}) }= a^{\frac{1}{6}}\\=\sqrt[6]{ a }\\---------------\)
4. \(\left(q^{\frac{5}{3}}\right)^{\frac{5}{3}}\\= q^{ \frac{5}{3} . \frac{5}{3} }= q^{\frac{25}{9}}\\=\sqrt[9]{ q^{25} }=q^{2}.\sqrt[9]{ q^{7} }\\---------------\)
5. \(\left(q^{\frac{-4}{5}}\right)^{-1}\\= q^{ \frac{-4}{5} . (-1) }= q^{\frac{4}{5}}\\=\sqrt[5]{ q^{4} }\\---------------\)
6. \(\left(q^{\frac{-1}{3}}\right)^{1}\\= q^{ \frac{-1}{3} . 1 }= q^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ q }}=\frac{1}{\sqrt[3]{ q }}. \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q}\\---------------\)
7. \(\left(x^{\frac{-4}{3}}\right)^{\frac{5}{6}}\\= x^{ \frac{-4}{3} . \frac{5}{6} }= x^{\frac{-10}{9}}\\=\frac{1}{\sqrt[9]{ x^{10} }}\\=\frac{1}{x.\sqrt[9]{ x }}=\frac{1}{x.\sqrt[9]{ x }} \color{purple}{\frac{\sqrt[9]{ x^{8} }}{\sqrt[9]{ x^{8} }}} \\=\frac{\sqrt[9]{ x^{8} }}{x^{2}}\\---------------\)
8. \(\left(a^{\frac{-1}{3}}\right)^{\frac{1}{2}}\\= a^{ \frac{-1}{3} . \frac{1}{2} }= a^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ a }}=\frac{1}{\sqrt[6]{ a }}. \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a|}\\---------------\)
9. \(\left(a^{\frac{1}{2}}\right)^{1}\\= a^{ \frac{1}{2} . 1 }= a^{\frac{1}{2}}\\= \sqrt{ a } \\---------------\)
10. \(\left(q^{\frac{5}{4}}\right)^{\frac{1}{6}}\\= q^{ \frac{5}{4} . \frac{1}{6} }= q^{\frac{5}{24}}\\=\sqrt[24]{ q^{5} }\\---------------\)
11. \(\left(q^{\frac{5}{3}}\right)^{\frac{-4}{5}}\\= q^{ \frac{5}{3} . (\frac{-4}{5}) }= q^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ q^{4} }}\\=\frac{1}{q.\sqrt[3]{ q }}=\frac{1}{q.\sqrt[3]{ q }} \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q^{2}}\\---------------\)
12. \(\left(y^{\frac{2}{3}}\right)^{\frac{-1}{6}}\\= y^{ \frac{2}{3} . (\frac{-1}{6}) }= y^{\frac{-1}{9}}\\=\frac{1}{\sqrt[9]{ y }}=\frac{1}{\sqrt[9]{ y }}. \color{purple}{\frac{\sqrt[9]{ y^{8} }}{\sqrt[9]{ y^{8} }}} \\=\frac{\sqrt[9]{ y^{8} }}{y}\\---------------\)