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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{\frac{1}{2}}\right)^{\frac{-2}{3}}\\= x^{ \frac{1}{2} . (\frac{-2}{3}) }= x^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ x }}=\frac{1}{\sqrt[3]{ x }}. \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x}\\---------------\)
2. \(\left(y^{\frac{1}{3}}\right)^{2}\\= y^{ \frac{1}{3} . 2 }= y^{\frac{2}{3}}\\=\sqrt[3]{ y^{2} }\\---------------\)
3. \(\left(x^{\frac{1}{5}}\right)^{\frac{-3}{4}}\\= x^{ \frac{1}{5} . (\frac{-3}{4}) }= x^{\frac{-3}{20}}\\=\frac{1}{\sqrt[20]{ x^{3} }}=\frac{1}{\sqrt[20]{ x^{3} }}. \color{purple}{\frac{\sqrt[20]{ x^{17} }}{\sqrt[20]{ x^{17} }}} \\=\frac{\sqrt[20]{ x^{17} }}{|x|}\\---------------\)
4. \(\left(a^{\frac{3}{2}}\right)^{\frac{5}{2}}\\= a^{ \frac{3}{2} . \frac{5}{2} }= a^{\frac{15}{4}}\\=\sqrt[4]{ a^{15} }=|a^{3}|.\sqrt[4]{ a^{3} }\\---------------\)
5. \(\left(q^{\frac{-3}{5}}\right)^{\frac{5}{4}}\\= q^{ \frac{-3}{5} . \frac{5}{4} }= q^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ q^{3} }}=\frac{1}{\sqrt[4]{ q^{3} }}. \color{purple}{\frac{\sqrt[4]{ q }}{\sqrt[4]{ q }}} \\=\frac{\sqrt[4]{ q }}{|q|}\\---------------\)
6. \(\left(a^{\frac{2}{5}}\right)^{\frac{5}{4}}\\= a^{ \frac{2}{5} . \frac{5}{4} }= a^{\frac{1}{2}}\\= \sqrt{ a } \\---------------\)
7. \(\left(a^{1}\right)^{\frac{-3}{5}}\\= a^{ 1 . (\frac{-3}{5}) }= a^{\frac{-3}{5}}\\=\frac{1}{\sqrt[5]{ a^{3} }}=\frac{1}{\sqrt[5]{ a^{3} }}. \color{purple}{\frac{\sqrt[5]{ a^{2} }}{\sqrt[5]{ a^{2} }}} \\=\frac{\sqrt[5]{ a^{2} }}{a}\\---------------\)
8. \(\left(a^{\frac{-1}{4}}\right)^{\frac{5}{3}}\\= a^{ \frac{-1}{4} . \frac{5}{3} }= a^{\frac{-5}{12}}\\=\frac{1}{\sqrt[12]{ a^{5} }}=\frac{1}{\sqrt[12]{ a^{5} }}. \color{purple}{\frac{\sqrt[12]{ a^{7} }}{\sqrt[12]{ a^{7} }}} \\=\frac{\sqrt[12]{ a^{7} }}{|a|}\\---------------\)
9. \(\left(y^{\frac{-5}{2}}\right)^{-1}\\= y^{ \frac{-5}{2} . (-1) }= y^{\frac{5}{2}}\\= \sqrt{ y^{5} } =|y^{2}|. \sqrt{ y } \\---------------\)
10. \(\left(a^{\frac{5}{2}}\right)^{\frac{-1}{2}}\\= a^{ \frac{5}{2} . (\frac{-1}{2}) }= a^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ a^{5} }}\\=\frac{1}{|a|.\sqrt[4]{ a }}=\frac{1}{|a|.\sqrt[4]{ a }} \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a^{2}|}\\---------------\)
11. \(\left(y^{\frac{-1}{2}}\right)^{\frac{1}{3}}\\= y^{ \frac{-1}{2} . \frac{1}{3} }= y^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ y }}=\frac{1}{\sqrt[6]{ y }}. \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y|}\\---------------\)
12. \(\left(y^{\frac{-3}{5}}\right)^{\frac{1}{2}}\\= y^{ \frac{-3}{5} . \frac{1}{2} }= y^{\frac{-3}{10}}\\=\frac{1}{\sqrt[10]{ y^{3} }}=\frac{1}{\sqrt[10]{ y^{3} }}. \color{purple}{\frac{\sqrt[10]{ y^{7} }}{\sqrt[10]{ y^{7} }}} \\=\frac{\sqrt[10]{ y^{7} }}{|y|}\\---------------\)