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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(a^{\frac{-2}{3}}\right)^{\frac{3}{2}}\\= a^{ \frac{-2}{3} . \frac{3}{2} }= a^{-1}\\=\frac{1}{a}\\---------------\)
2. \(\left(x^{\frac{1}{4}}\right)^{\frac{-1}{3}}\\= x^{ \frac{1}{4} . (\frac{-1}{3}) }= x^{\frac{-1}{12}}\\=\frac{1}{\sqrt[12]{ x }}=\frac{1}{\sqrt[12]{ x }}. \color{purple}{\frac{\sqrt[12]{ x^{11} }}{\sqrt[12]{ x^{11} }}} \\=\frac{\sqrt[12]{ x^{11} }}{|x|}\\---------------\)
3. \(\left(y^{\frac{2}{5}}\right)^{-1}\\= y^{ \frac{2}{5} . (-1) }= y^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ y^{2} }}=\frac{1}{\sqrt[5]{ y^{2} }}. \color{purple}{\frac{\sqrt[5]{ y^{3} }}{\sqrt[5]{ y^{3} }}} \\=\frac{\sqrt[5]{ y^{3} }}{y}\\---------------\)
4. \(\left(y^{-1}\right)^{\frac{1}{3}}\\= y^{ -1 . \frac{1}{3} }= y^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ y }}=\frac{1}{\sqrt[3]{ y }}. \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y}\\---------------\)
5. \(\left(a^{\frac{-3}{5}}\right)^{\frac{3}{5}}\\= a^{ \frac{-3}{5} . \frac{3}{5} }= a^{\frac{-9}{25}}\\=\frac{1}{\sqrt[25]{ a^{9} }}=\frac{1}{\sqrt[25]{ a^{9} }}. \color{purple}{\frac{\sqrt[25]{ a^{16} }}{\sqrt[25]{ a^{16} }}} \\=\frac{\sqrt[25]{ a^{16} }}{a}\\---------------\)
6. \(\left(x^{\frac{-2}{5}}\right)^{\frac{1}{3}}\\= x^{ \frac{-2}{5} . \frac{1}{3} }= x^{\frac{-2}{15}}\\=\frac{1}{\sqrt[15]{ x^{2} }}=\frac{1}{\sqrt[15]{ x^{2} }}. \color{purple}{\frac{\sqrt[15]{ x^{13} }}{\sqrt[15]{ x^{13} }}} \\=\frac{\sqrt[15]{ x^{13} }}{x}\\---------------\)
7. \(\left(a^{\frac{-3}{5}}\right)^{\frac{2}{3}}\\= a^{ \frac{-3}{5} . \frac{2}{3} }= a^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ a^{2} }}=\frac{1}{\sqrt[5]{ a^{2} }}. \color{purple}{\frac{\sqrt[5]{ a^{3} }}{\sqrt[5]{ a^{3} }}} \\=\frac{\sqrt[5]{ a^{3} }}{a}\\---------------\)
8. \(\left(y^{1}\right)^{\frac{4}{5}}\\= y^{ 1 . \frac{4}{5} }= y^{\frac{4}{5}}\\=\sqrt[5]{ y^{4} }\\---------------\)
9. \(\left(q^{\frac{1}{2}}\right)^{\frac{2}{3}}\\= q^{ \frac{1}{2} . \frac{2}{3} }= q^{\frac{1}{3}}\\=\sqrt[3]{ q }\\---------------\)
10. \(\left(y^{\frac{5}{4}}\right)^{\frac{-2}{3}}\\= y^{ \frac{5}{4} . (\frac{-2}{3}) }= y^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ y^{5} }}=\frac{1}{\sqrt[6]{ y^{5} }}. \color{purple}{\frac{\sqrt[6]{ y }}{\sqrt[6]{ y }}} \\=\frac{\sqrt[6]{ y }}{|y|}\\---------------\)
11. \(\left(y^{\frac{-1}{2}}\right)^{\frac{-5}{3}}\\= y^{ \frac{-1}{2} . (\frac{-5}{3}) }= y^{\frac{5}{6}}\\=\sqrt[6]{ y^{5} }\\---------------\)
12. \(\left(x^{\frac{-1}{2}}\right)^{\frac{-5}{4}}\\= x^{ \frac{-1}{2} . (\frac{-5}{4}) }= x^{\frac{5}{8}}\\=\sqrt[8]{ x^{5} }\\---------------\)