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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(a^{\frac{-1}{4}}\right)^{\frac{-4}{5}}\\= a^{ \frac{-1}{4} . (\frac{-4}{5}) }= a^{\frac{1}{5}}\\=\sqrt[5]{ a }\\---------------\)
2. \(\left(a^{-2}\right)^{\frac{5}{3}}\\= a^{ -2 . \frac{5}{3} }= a^{\frac{-10}{3}}\\=\frac{1}{\sqrt[3]{ a^{10} }}\\=\frac{1}{a^{3}.\sqrt[3]{ a }}=\frac{1}{a^{3}.\sqrt[3]{ a }} \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a^{4}}\\---------------\)
3. \(\left(a^{-1}\right)^{\frac{-1}{3}}\\= a^{ -1 . (\frac{-1}{3}) }= a^{\frac{1}{3}}\\=\sqrt[3]{ a }\\---------------\)
4. \(\left(x^{\frac{4}{3}}\right)^{\frac{2}{5}}\\= x^{ \frac{4}{3} . \frac{2}{5} }= x^{\frac{8}{15}}\\=\sqrt[15]{ x^{8} }\\---------------\)
5. \(\left(y^{\frac{-5}{6}}\right)^{\frac{-3}{4}}\\= y^{ \frac{-5}{6} . (\frac{-3}{4}) }= y^{\frac{5}{8}}\\=\sqrt[8]{ y^{5} }\\---------------\)
6. \(\left(y^{\frac{-1}{3}}\right)^{\frac{-5}{6}}\\= y^{ \frac{-1}{3} . (\frac{-5}{6}) }= y^{\frac{5}{18}}\\=\sqrt[18]{ y^{5} }\\---------------\)
7. \(\left(a^{\frac{1}{4}}\right)^{\frac{-5}{4}}\\= a^{ \frac{1}{4} . (\frac{-5}{4}) }= a^{\frac{-5}{16}}\\=\frac{1}{\sqrt[16]{ a^{5} }}=\frac{1}{\sqrt[16]{ a^{5} }}. \color{purple}{\frac{\sqrt[16]{ a^{11} }}{\sqrt[16]{ a^{11} }}} \\=\frac{\sqrt[16]{ a^{11} }}{|a|}\\---------------\)
8. \(\left(q^{\frac{-5}{2}}\right)^{\frac{2}{3}}\\= q^{ \frac{-5}{2} . \frac{2}{3} }= q^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ q^{5} }}\\=\frac{1}{q.\sqrt[3]{ q^{2} }}=\frac{1}{q.\sqrt[3]{ q^{2} }} \color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q^{2}}\\---------------\)
9. \(\left(y^{\frac{-2}{3}}\right)^{\frac{4}{3}}\\= y^{ \frac{-2}{3} . \frac{4}{3} }= y^{\frac{-8}{9}}\\=\frac{1}{\sqrt[9]{ y^{8} }}=\frac{1}{\sqrt[9]{ y^{8} }}. \color{purple}{\frac{\sqrt[9]{ y }}{\sqrt[9]{ y }}} \\=\frac{\sqrt[9]{ y }}{y}\\---------------\)
10. \(\left(y^{\frac{1}{4}}\right)^{\frac{3}{2}}\\= y^{ \frac{1}{4} . \frac{3}{2} }= y^{\frac{3}{8}}\\=\sqrt[8]{ y^{3} }\\---------------\)
11. \(\left(x^{\frac{-2}{5}}\right)^{\frac{3}{2}}\\= x^{ \frac{-2}{5} . \frac{3}{2} }= x^{\frac{-3}{5}}\\=\frac{1}{\sqrt[5]{ x^{3} }}=\frac{1}{\sqrt[5]{ x^{3} }}. \color{purple}{\frac{\sqrt[5]{ x^{2} }}{\sqrt[5]{ x^{2} }}} \\=\frac{\sqrt[5]{ x^{2} }}{x}\\---------------\)
12. \(\left(y^{\frac{1}{4}}\right)^{\frac{1}{2}}\\= y^{ \frac{1}{4} . \frac{1}{2} }= y^{\frac{1}{8}}\\=\sqrt[8]{ y }\\---------------\)