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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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