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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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