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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(a^{\frac{-3}{4}}\right)^{\frac{-4}{3}}\\= a^{ \frac{-3}{4} . (\frac{-4}{3}) }= a^{1}\\\\---------------\)
2. \(\left(q^{\frac{3}{5}}\right)^{\frac{-1}{5}}\\= q^{ \frac{3}{5} . (\frac{-1}{5}) }= q^{\frac{-3}{25}}\\=\frac{1}{\sqrt[25]{ q^{3} }}=\frac{1}{\sqrt[25]{ q^{3} }}. \color{purple}{\frac{\sqrt[25]{ q^{22} }}{\sqrt[25]{ q^{22} }}} \\=\frac{\sqrt[25]{ q^{22} }}{q}\\---------------\)
3. \(\left(y^{1}\right)^{\frac{1}{6}}\\= y^{ 1 . \frac{1}{6} }= y^{\frac{1}{6}}\\=\sqrt[6]{ y }\\---------------\)
4. \(\left(x^{\frac{-5}{4}}\right)^{1}\\= x^{ \frac{-5}{4} . 1 }= x^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ x^{5} }}\\=\frac{1}{|x|.\sqrt[4]{ x }}=\frac{1}{|x|.\sqrt[4]{ x }} \color{purple}{\frac{\sqrt[4]{ x^{3} }}{\sqrt[4]{ x^{3} }}} \\=\frac{\sqrt[4]{ x^{3} }}{|x^{2}|}\\---------------\)
5. \(\left(y^{\frac{1}{2}}\right)^{\frac{-5}{4}}\\= y^{ \frac{1}{2} . (\frac{-5}{4}) }= y^{\frac{-5}{8}}\\=\frac{1}{\sqrt[8]{ y^{5} }}=\frac{1}{\sqrt[8]{ y^{5} }}. \color{purple}{\frac{\sqrt[8]{ y^{3} }}{\sqrt[8]{ y^{3} }}} \\=\frac{\sqrt[8]{ y^{3} }}{|y|}\\---------------\)
6. \(\left(x^{\frac{5}{3}}\right)^{\frac{-1}{3}}\\= x^{ \frac{5}{3} . (\frac{-1}{3}) }= x^{\frac{-5}{9}}\\=\frac{1}{\sqrt[9]{ x^{5} }}=\frac{1}{\sqrt[9]{ x^{5} }}. \color{purple}{\frac{\sqrt[9]{ x^{4} }}{\sqrt[9]{ x^{4} }}} \\=\frac{\sqrt[9]{ x^{4} }}{x}\\---------------\)
7. \(\left(x^{\frac{-1}{3}}\right)^{\frac{-5}{4}}\\= x^{ \frac{-1}{3} . (\frac{-5}{4}) }= x^{\frac{5}{12}}\\=\sqrt[12]{ x^{5} }\\---------------\)
8. \(\left(x^{\frac{1}{6}}\right)^{\frac{1}{4}}\\= x^{ \frac{1}{6} . \frac{1}{4} }= x^{\frac{1}{24}}\\=\sqrt[24]{ x }\\---------------\)
9. \(\left(q^{-1}\right)^{\frac{-2}{5}}\\= q^{ -1 . (\frac{-2}{5}) }= q^{\frac{2}{5}}\\=\sqrt[5]{ q^{2} }\\---------------\)
10. \(\left(q^{\frac{3}{4}}\right)^{\frac{5}{2}}\\= q^{ \frac{3}{4} . \frac{5}{2} }= q^{\frac{15}{8}}\\=\sqrt[8]{ q^{15} }=|q|.\sqrt[8]{ q^{7} }\\---------------\)
11. \(\left(q^{\frac{-1}{2}}\right)^{\frac{-2}{3}}\\= q^{ \frac{-1}{2} . (\frac{-2}{3}) }= q^{\frac{1}{3}}\\=\sqrt[3]{ q }\\---------------\)
12. \(\left(a^{\frac{-3}{4}}\right)^{\frac{5}{4}}\\= a^{ \frac{-3}{4} . \frac{5}{4} }= a^{\frac{-15}{16}}\\=\frac{1}{\sqrt[16]{ a^{15} }}=\frac{1}{\sqrt[16]{ a^{15} }}. \color{purple}{\frac{\sqrt[16]{ a }}{\sqrt[16]{ a }}} \\=\frac{\sqrt[16]{ a }}{|a|}\\---------------\)