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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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