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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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