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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(y^{\frac{-5}{3}}\right)^{\frac{-2}{3}}\\= y^{ \frac{-5}{3} . (\frac{-2}{3}) }= y^{\frac{10}{9}}\\=\sqrt[9]{ y^{10} }=y.\sqrt[9]{ y }\\---------------\)
2. \(\left(a^{-1}\right)^{\frac{-3}{5}}\\= a^{ -1 . (\frac{-3}{5}) }= a^{\frac{3}{5}}\\=\sqrt[5]{ a^{3} }\\---------------\)
3. \(\left(x^{\frac{1}{5}}\right)^{\frac{-1}{2}}\\= x^{ \frac{1}{5} . (\frac{-1}{2}) }= x^{\frac{-1}{10}}\\=\frac{1}{\sqrt[10]{ x }}=\frac{1}{\sqrt[10]{ x }}. \color{purple}{\frac{\sqrt[10]{ x^{9} }}{\sqrt[10]{ x^{9} }}} \\=\frac{\sqrt[10]{ x^{9} }}{|x|}\\---------------\)
4. \(\left(y^{-2}\right)^{\frac{-4}{3}}\\= y^{ -2 . (\frac{-4}{3}) }= y^{\frac{8}{3}}\\=\sqrt[3]{ y^{8} }=y^{2}.\sqrt[3]{ y^{2} }\\---------------\)
5. \(\left(q^{\frac{1}{5}}\right)^{\frac{-1}{5}}\\= q^{ \frac{1}{5} . (\frac{-1}{5}) }= q^{\frac{-1}{25}}\\=\frac{1}{\sqrt[25]{ q }}=\frac{1}{\sqrt[25]{ q }}. \color{purple}{\frac{\sqrt[25]{ q^{24} }}{\sqrt[25]{ q^{24} }}} \\=\frac{\sqrt[25]{ q^{24} }}{q}\\---------------\)
6. \(\left(x^{-1}\right)^{\frac{-1}{4}}\\= x^{ -1 . (\frac{-1}{4}) }= x^{\frac{1}{4}}\\=\sqrt[4]{ x }\\---------------\)
7. \(\left(q^{\frac{4}{5}}\right)^{\frac{-1}{2}}\\= q^{ \frac{4}{5} . (\frac{-1}{2}) }= q^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ q^{2} }}=\frac{1}{\sqrt[5]{ q^{2} }}. \color{purple}{\frac{\sqrt[5]{ q^{3} }}{\sqrt[5]{ q^{3} }}} \\=\frac{\sqrt[5]{ q^{3} }}{q}\\---------------\)
8. \(\left(a^{\frac{-1}{5}}\right)^{\frac{-1}{2}}\\= a^{ \frac{-1}{5} . (\frac{-1}{2}) }= a^{\frac{1}{10}}\\=\sqrt[10]{ a }\\---------------\)
9. \(\left(a^{\frac{-1}{4}}\right)^{\frac{4}{3}}\\= a^{ \frac{-1}{4} . \frac{4}{3} }= a^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ a }}=\frac{1}{\sqrt[3]{ a }}. \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a}\\---------------\)
10. \(\left(a^{\frac{1}{5}}\right)^{\frac{5}{3}}\\= a^{ \frac{1}{5} . \frac{5}{3} }= a^{\frac{1}{3}}\\=\sqrt[3]{ a }\\---------------\)
11. \(\left(a^{\frac{2}{3}}\right)^{-1}\\= a^{ \frac{2}{3} . (-1) }= a^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ a^{2} }}=\frac{1}{\sqrt[3]{ a^{2} }}. \color{purple}{\frac{\sqrt[3]{ a }}{\sqrt[3]{ a }}} \\=\frac{\sqrt[3]{ a }}{a}\\---------------\)
12. \(\left(y^{\frac{1}{4}}\right)^{\frac{4}{5}}\\= y^{ \frac{1}{4} . \frac{4}{5} }= y^{\frac{1}{5}}\\=\sqrt[5]{ y }\\---------------\)