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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(q^{1}\right)^{\frac{4}{5}}\\= q^{ 1 . \frac{4}{5} }= q^{\frac{4}{5}}\\=\sqrt[5]{ q^{4} }\\---------------\)
2. \(\left(a^{\frac{1}{2}}\right)^{\frac{-5}{3}}\\= a^{ \frac{1}{2} . (\frac{-5}{3}) }= a^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ a^{5} }}=\frac{1}{\sqrt[6]{ a^{5} }}. \color{purple}{\frac{\sqrt[6]{ a }}{\sqrt[6]{ a }}} \\=\frac{\sqrt[6]{ a }}{|a|}\\---------------\)
3. \(\left(q^{\frac{-1}{4}}\right)^{\frac{5}{6}}\\= q^{ \frac{-1}{4} . \frac{5}{6} }= q^{\frac{-5}{24}}\\=\frac{1}{\sqrt[24]{ q^{5} }}=\frac{1}{\sqrt[24]{ q^{5} }}. \color{purple}{\frac{\sqrt[24]{ q^{19} }}{\sqrt[24]{ q^{19} }}} \\=\frac{\sqrt[24]{ q^{19} }}{|q|}\\---------------\)
4. \(\left(a^{\frac{3}{5}}\right)^{\frac{-1}{2}}\\= a^{ \frac{3}{5} . (\frac{-1}{2}) }= a^{\frac{-3}{10}}\\=\frac{1}{\sqrt[10]{ a^{3} }}=\frac{1}{\sqrt[10]{ a^{3} }}. \color{purple}{\frac{\sqrt[10]{ a^{7} }}{\sqrt[10]{ a^{7} }}} \\=\frac{\sqrt[10]{ a^{7} }}{|a|}\\---------------\)
5. \(\left(a^{\frac{-4}{5}}\right)^{\frac{-3}{5}}\\= a^{ \frac{-4}{5} . (\frac{-3}{5}) }= a^{\frac{12}{25}}\\=\sqrt[25]{ a^{12} }\\---------------\)
6. \(\left(q^{-2}\right)^{\frac{3}{2}}\\= q^{ -2 . \frac{3}{2} }= q^{-3}\\=\frac{1}{q^{3}}\\---------------\)
7. \(\left(q^{\frac{-1}{3}}\right)^{\frac{1}{5}}\\= q^{ \frac{-1}{3} . \frac{1}{5} }= q^{\frac{-1}{15}}\\=\frac{1}{\sqrt[15]{ q }}=\frac{1}{\sqrt[15]{ q }}. \color{purple}{\frac{\sqrt[15]{ q^{14} }}{\sqrt[15]{ q^{14} }}} \\=\frac{\sqrt[15]{ q^{14} }}{q}\\---------------\)
8. \(\left(y^{\frac{-3}{4}}\right)^{\frac{-4}{3}}\\= y^{ \frac{-3}{4} . (\frac{-4}{3}) }= y^{1}\\\\---------------\)
9. \(\left(y^{\frac{-5}{3}}\right)^{\frac{-1}{3}}\\= y^{ \frac{-5}{3} . (\frac{-1}{3}) }= y^{\frac{5}{9}}\\=\sqrt[9]{ y^{5} }\\---------------\)
10. \(\left(q^{\frac{3}{2}}\right)^{\frac{1}{6}}\\= q^{ \frac{3}{2} . \frac{1}{6} }= q^{\frac{1}{4}}\\=\sqrt[4]{ q }\\---------------\)
11. \(\left(x^{\frac{-5}{6}}\right)^{\frac{-1}{4}}\\= x^{ \frac{-5}{6} . (\frac{-1}{4}) }= x^{\frac{5}{24}}\\=\sqrt[24]{ x^{5} }\\---------------\)
12. \(\left(x^{\frac{-4}{5}}\right)^{\frac{-1}{6}}\\= x^{ \frac{-4}{5} . (\frac{-1}{6}) }= x^{\frac{2}{15}}\\=\sqrt[15]{ x^{2} }\\---------------\)