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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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