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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(q^{\frac{-4}{3}}\right)^{\frac{-4}{5}}\\= q^{ \frac{-4}{3} . (\frac{-4}{5}) }= q^{\frac{16}{15}}\\=\sqrt[15]{ q^{16} }=q.\sqrt[15]{ q }\\---------------\)
2. \(\left(q^{\frac{3}{2}}\right)^{\frac{5}{6}}\\= q^{ \frac{3}{2} . \frac{5}{6} }= q^{\frac{5}{4}}\\=\sqrt[4]{ q^{5} }=|q|.\sqrt[4]{ q }\\---------------\)
3. \(\left(a^{\frac{4}{3}}\right)^{\frac{2}{3}}\\= a^{ \frac{4}{3} . \frac{2}{3} }= a^{\frac{8}{9}}\\=\sqrt[9]{ a^{8} }\\---------------\)
4. \(\left(q^{\frac{-3}{5}}\right)^{-1}\\= q^{ \frac{-3}{5} . (-1) }= q^{\frac{3}{5}}\\=\sqrt[5]{ q^{3} }\\---------------\)
5. \(\left(a^{\frac{3}{2}}\right)^{\frac{1}{2}}\\= a^{ \frac{3}{2} . \frac{1}{2} }= a^{\frac{3}{4}}\\=\sqrt[4]{ a^{3} }\\---------------\)
6. \(\left(a^{\frac{1}{4}}\right)^{\frac{-1}{6}}\\= a^{ \frac{1}{4} . (\frac{-1}{6}) }= a^{\frac{-1}{24}}\\=\frac{1}{\sqrt[24]{ a }}=\frac{1}{\sqrt[24]{ a }}. \color{purple}{\frac{\sqrt[24]{ a^{23} }}{\sqrt[24]{ a^{23} }}} \\=\frac{\sqrt[24]{ a^{23} }}{|a|}\\---------------\)
7. \(\left(y^{\frac{-4}{3}}\right)^{\frac{3}{2}}\\= y^{ \frac{-4}{3} . \frac{3}{2} }= y^{-2}\\=\frac{1}{y^{2}}\\---------------\)
8. \(\left(x^{\frac{1}{2}}\right)^{\frac{-1}{4}}\\= x^{ \frac{1}{2} . (\frac{-1}{4}) }= x^{\frac{-1}{8}}\\=\frac{1}{\sqrt[8]{ x }}=\frac{1}{\sqrt[8]{ x }}. \color{purple}{\frac{\sqrt[8]{ x^{7} }}{\sqrt[8]{ x^{7} }}} \\=\frac{\sqrt[8]{ x^{7} }}{|x|}\\---------------\)
9. \(\left(q^{\frac{1}{2}}\right)^{1}\\= q^{ \frac{1}{2} . 1 }= q^{\frac{1}{2}}\\= \sqrt{ q } \\---------------\)
10. \(\left(x^{1}\right)^{\frac{1}{2}}\\= x^{ 1 . \frac{1}{2} }= x^{\frac{1}{2}}\\= \sqrt{ x } \\---------------\)
11. \(\left(a^{1}\right)^{\frac{3}{5}}\\= a^{ 1 . \frac{3}{5} }= a^{\frac{3}{5}}\\=\sqrt[5]{ a^{3} }\\---------------\)
12. \(\left(x^{\frac{1}{6}}\right)^{\frac{-1}{2}}\\= x^{ \frac{1}{6} . (\frac{-1}{2}) }= x^{\frac{-1}{12}}\\=\frac{1}{\sqrt[12]{ x }}=\frac{1}{\sqrt[12]{ x }}. \color{purple}{\frac{\sqrt[12]{ x^{11} }}{\sqrt[12]{ x^{11} }}} \\=\frac{\sqrt[12]{ x^{11} }}{|x|}\\---------------\)