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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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