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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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