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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(a^{\frac{-4}{5}}\right)^{\frac{5}{3}}\\= a^{ \frac{-4}{5} . \frac{5}{3} }= a^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ a^{4} }}\\=\frac{1}{a.\sqrt[3]{ a }}=\frac{1}{a.\sqrt[3]{ a }} \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a^{2}}\\---------------\)
2. \(\left(q^{\frac{-1}{6}}\right)^{\frac{-1}{5}}\\= q^{ \frac{-1}{6} . (\frac{-1}{5}) }= q^{\frac{1}{30}}\\=\sqrt[30]{ q }\\---------------\)
3. \(\left(x^{\frac{-2}{3}}\right)^{-1}\\= x^{ \frac{-2}{3} . (-1) }= x^{\frac{2}{3}}\\=\sqrt[3]{ x^{2} }\\---------------\)
4. \(\left(y^{-2}\right)^{\frac{3}{2}}\\= y^{ -2 . \frac{3}{2} }= y^{-3}\\=\frac{1}{y^{3}}\\---------------\)
5. \(\left(q^{\frac{1}{3}}\right)^{\frac{-5}{2}}\\= q^{ \frac{1}{3} . (\frac{-5}{2}) }= q^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ q^{5} }}=\frac{1}{\sqrt[6]{ q^{5} }}. \color{purple}{\frac{\sqrt[6]{ q }}{\sqrt[6]{ q }}} \\=\frac{\sqrt[6]{ q }}{|q|}\\---------------\)
6. \(\left(q^{1}\right)^{\frac{1}{2}}\\= q^{ 1 . \frac{1}{2} }= q^{\frac{1}{2}}\\= \sqrt{ q } \\---------------\)
7. \(\left(q^{\frac{1}{2}}\right)^{\frac{5}{2}}\\= q^{ \frac{1}{2} . \frac{5}{2} }= q^{\frac{5}{4}}\\=\sqrt[4]{ q^{5} }=|q|.\sqrt[4]{ q }\\---------------\)
8. \(\left(a^{\frac{1}{2}}\right)^{\frac{-3}{5}}\\= a^{ \frac{1}{2} . (\frac{-3}{5}) }= a^{\frac{-3}{10}}\\=\frac{1}{\sqrt[10]{ a^{3} }}=\frac{1}{\sqrt[10]{ a^{3} }}. \color{purple}{\frac{\sqrt[10]{ a^{7} }}{\sqrt[10]{ a^{7} }}} \\=\frac{\sqrt[10]{ a^{7} }}{|a|}\\---------------\)
9. \(\left(q^{\frac{4}{5}}\right)^{\frac{1}{6}}\\= q^{ \frac{4}{5} . \frac{1}{6} }= q^{\frac{2}{15}}\\=\sqrt[15]{ q^{2} }\\---------------\)
10. \(\left(y^{\frac{5}{4}}\right)^{\frac{1}{4}}\\= y^{ \frac{5}{4} . \frac{1}{4} }= y^{\frac{5}{16}}\\=\sqrt[16]{ y^{5} }\\---------------\)
11. \(\left(a^{\frac{1}{3}}\right)^{\frac{-3}{4}}\\= a^{ \frac{1}{3} . (\frac{-3}{4}) }= a^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ a }}=\frac{1}{\sqrt[4]{ a }}. \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a|}\\---------------\)
12. \(\left(a^{\frac{-3}{4}}\right)^{\frac{-5}{4}}\\= a^{ \frac{-3}{4} . (\frac{-5}{4}) }= a^{\frac{15}{16}}\\=\sqrt[16]{ a^{15} }\\---------------\)