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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{\frac{1}{2}}\right)^{\frac{-1}{2}}\\= x^{ \frac{1}{2} . (\frac{-1}{2}) }= x^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ x }}=\frac{1}{\sqrt[4]{ x }}. \color{purple}{\frac{\sqrt[4]{ x^{3} }}{\sqrt[4]{ x^{3} }}} \\=\frac{\sqrt[4]{ x^{3} }}{|x|}\\---------------\)
2. \(\left(q^{\frac{1}{2}}\right)^{\frac{5}{2}}\\= q^{ \frac{1}{2} . \frac{5}{2} }= q^{\frac{5}{4}}\\=\sqrt[4]{ q^{5} }=|q|.\sqrt[4]{ q }\\---------------\)
3. \(\left(q^{\frac{1}{2}}\right)^{\frac{-4}{3}}\\= q^{ \frac{1}{2} . (\frac{-4}{3}) }= q^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ q^{2} }}=\frac{1}{\sqrt[3]{ q^{2} }}. \color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q}\\---------------\)
4. \(\left(y^{\frac{1}{3}}\right)^{-2}\\= y^{ \frac{1}{3} . (-2) }= y^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ y^{2} }}=\frac{1}{\sqrt[3]{ y^{2} }}. \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y}\\---------------\)
5. \(\left(q^{1}\right)^{\frac{2}{3}}\\= q^{ 1 . \frac{2}{3} }= q^{\frac{2}{3}}\\=\sqrt[3]{ q^{2} }\\---------------\)
6. \(\left(a^{\frac{1}{4}}\right)^{\frac{-1}{3}}\\= a^{ \frac{1}{4} . (\frac{-1}{3}) }= a^{\frac{-1}{12}}\\=\frac{1}{\sqrt[12]{ a }}=\frac{1}{\sqrt[12]{ a }}. \color{purple}{\frac{\sqrt[12]{ a^{11} }}{\sqrt[12]{ a^{11} }}} \\=\frac{\sqrt[12]{ a^{11} }}{|a|}\\---------------\)
7. \(\left(a^{\frac{1}{5}}\right)^{\frac{-3}{4}}\\= a^{ \frac{1}{5} . (\frac{-3}{4}) }= a^{\frac{-3}{20}}\\=\frac{1}{\sqrt[20]{ a^{3} }}=\frac{1}{\sqrt[20]{ a^{3} }}. \color{purple}{\frac{\sqrt[20]{ a^{17} }}{\sqrt[20]{ a^{17} }}} \\=\frac{\sqrt[20]{ a^{17} }}{|a|}\\---------------\)
8. \(\left(y^{\frac{-1}{3}}\right)^{\frac{3}{4}}\\= y^{ \frac{-1}{3} . \frac{3}{4} }= y^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ y }}=\frac{1}{\sqrt[4]{ y }}. \color{purple}{\frac{\sqrt[4]{ y^{3} }}{\sqrt[4]{ y^{3} }}} \\=\frac{\sqrt[4]{ y^{3} }}{|y|}\\---------------\)
9. \(\left(x^{1}\right)^{\frac{2}{5}}\\= x^{ 1 . \frac{2}{5} }= x^{\frac{2}{5}}\\=\sqrt[5]{ x^{2} }\\---------------\)
10. \(\left(a^{1}\right)^{\frac{-5}{4}}\\= a^{ 1 . (\frac{-5}{4}) }= a^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ a^{5} }}\\=\frac{1}{|a|.\sqrt[4]{ a }}=\frac{1}{|a|.\sqrt[4]{ a }} \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a^{2}|}\\---------------\)
11. \(\left(x^{\frac{-1}{4}}\right)^{\frac{5}{6}}\\= x^{ \frac{-1}{4} . \frac{5}{6} }= x^{\frac{-5}{24}}\\=\frac{1}{\sqrt[24]{ x^{5} }}=\frac{1}{\sqrt[24]{ x^{5} }}. \color{purple}{\frac{\sqrt[24]{ x^{19} }}{\sqrt[24]{ x^{19} }}} \\=\frac{\sqrt[24]{ x^{19} }}{|x|}\\---------------\)
12. \(\left(a^{\frac{1}{2}}\right)^{\frac{3}{5}}\\= a^{ \frac{1}{2} . \frac{3}{5} }= a^{\frac{3}{10}}\\=\sqrt[10]{ a^{3} }\\---------------\)