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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{\frac{5}{3}}\right)^{\frac{5}{4}}\\= x^{ \frac{5}{3} . \frac{5}{4} }= x^{\frac{25}{12}}\\=\sqrt[12]{ x^{25} }=|x^{2}|.\sqrt[12]{ x }\\---------------\)
2. \(\left(a^{\frac{1}{2}}\right)^{\frac{-3}{4}}\\= a^{ \frac{1}{2} . (\frac{-3}{4}) }= a^{\frac{-3}{8}}\\=\frac{1}{\sqrt[8]{ a^{3} }}=\frac{1}{\sqrt[8]{ a^{3} }}. \color{purple}{\frac{\sqrt[8]{ a^{5} }}{\sqrt[8]{ a^{5} }}} \\=\frac{\sqrt[8]{ a^{5} }}{|a|}\\---------------\)
3. \(\left(y^{\frac{1}{2}}\right)^{\frac{1}{5}}\\= y^{ \frac{1}{2} . \frac{1}{5} }= y^{\frac{1}{10}}\\=\sqrt[10]{ y }\\---------------\)
4. \(\left(x^{1}\right)^{\frac{-3}{4}}\\= x^{ 1 . (\frac{-3}{4}) }= x^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ x^{3} }}=\frac{1}{\sqrt[4]{ x^{3} }}. \color{purple}{\frac{\sqrt[4]{ x }}{\sqrt[4]{ x }}} \\=\frac{\sqrt[4]{ x }}{|x|}\\---------------\)
5. \(\left(a^{\frac{-5}{2}}\right)^{\frac{-1}{2}}\\= a^{ \frac{-5}{2} . (\frac{-1}{2}) }= a^{\frac{5}{4}}\\=\sqrt[4]{ a^{5} }=|a|.\sqrt[4]{ a }\\---------------\)
6. \(\left(x^{1}\right)^{\frac{5}{3}}\\= x^{ 1 . \frac{5}{3} }= x^{\frac{5}{3}}\\=\sqrt[3]{ x^{5} }=x.\sqrt[3]{ x^{2} }\\---------------\)
7. \(\left(q^{\frac{-1}{3}}\right)^{\frac{5}{2}}\\= q^{ \frac{-1}{3} . \frac{5}{2} }= q^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ q^{5} }}=\frac{1}{\sqrt[6]{ q^{5} }}. \color{purple}{\frac{\sqrt[6]{ q }}{\sqrt[6]{ q }}} \\=\frac{\sqrt[6]{ q }}{|q|}\\---------------\)
8. \(\left(x^{\frac{1}{3}}\right)^{\frac{4}{5}}\\= x^{ \frac{1}{3} . \frac{4}{5} }= x^{\frac{4}{15}}\\=\sqrt[15]{ x^{4} }\\---------------\)
9. \(\left(y^{-1}\right)^{\frac{1}{3}}\\= y^{ -1 . \frac{1}{3} }= y^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ y }}=\frac{1}{\sqrt[3]{ y }}. \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y}\\---------------\)
10. \(\left(q^{\frac{3}{4}}\right)^{\frac{-1}{3}}\\= q^{ \frac{3}{4} . (\frac{-1}{3}) }= q^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ q }}=\frac{1}{\sqrt[4]{ q }}. \color{purple}{\frac{\sqrt[4]{ q^{3} }}{\sqrt[4]{ q^{3} }}} \\=\frac{\sqrt[4]{ q^{3} }}{|q|}\\---------------\)
11. \(\left(y^{\frac{-4}{5}}\right)^{\frac{1}{2}}\\= y^{ \frac{-4}{5} . \frac{1}{2} }= y^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ y^{2} }}=\frac{1}{\sqrt[5]{ y^{2} }}. \color{purple}{\frac{\sqrt[5]{ y^{3} }}{\sqrt[5]{ y^{3} }}} \\=\frac{\sqrt[5]{ y^{3} }}{y}\\---------------\)
12. \(\left(a^{\frac{-1}{2}}\right)^{\frac{-2}{5}}\\= a^{ \frac{-1}{2} . (\frac{-2}{5}) }= a^{\frac{1}{5}}\\=\sqrt[5]{ a }\\---------------\)