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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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