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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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