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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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