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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(y^{\frac{-4}{3}}\right)^{1}\\= y^{ \frac{-4}{3} . 1 }= y^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ y^{4} }}\\=\frac{1}{y.\sqrt[3]{ y }}=\frac{1}{y.\sqrt[3]{ y }} \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y^{2}}\\---------------\)
2. \(\left(x^{\frac{3}{4}}\right)^{\frac{-5}{4}}\\= x^{ \frac{3}{4} . (\frac{-5}{4}) }= x^{\frac{-15}{16}}\\=\frac{1}{\sqrt[16]{ x^{15} }}=\frac{1}{\sqrt[16]{ x^{15} }}. \color{purple}{\frac{\sqrt[16]{ x }}{\sqrt[16]{ x }}} \\=\frac{\sqrt[16]{ x }}{|x|}\\---------------\)
3. \(\left(q^{\frac{-5}{6}}\right)^{\frac{-5}{3}}\\= q^{ \frac{-5}{6} . (\frac{-5}{3}) }= q^{\frac{25}{18}}\\=\sqrt[18]{ q^{25} }=|q|.\sqrt[18]{ q^{7} }\\---------------\)
4. \(\left(x^{\frac{-1}{6}}\right)^{\frac{4}{3}}\\= x^{ \frac{-1}{6} . \frac{4}{3} }= x^{\frac{-2}{9}}\\=\frac{1}{\sqrt[9]{ x^{2} }}=\frac{1}{\sqrt[9]{ x^{2} }}. \color{purple}{\frac{\sqrt[9]{ x^{7} }}{\sqrt[9]{ x^{7} }}} \\=\frac{\sqrt[9]{ x^{7} }}{x}\\---------------\)
5. \(\left(q^{-1}\right)^{\frac{-1}{6}}\\= q^{ -1 . (\frac{-1}{6}) }= q^{\frac{1}{6}}\\=\sqrt[6]{ q }\\---------------\)
6. \(\left(x^{\frac{1}{6}}\right)^{\frac{5}{3}}\\= x^{ \frac{1}{6} . \frac{5}{3} }= x^{\frac{5}{18}}\\=\sqrt[18]{ x^{5} }\\---------------\)
7. \(\left(q^{\frac{-3}{5}}\right)^{\frac{-1}{2}}\\= q^{ \frac{-3}{5} . (\frac{-1}{2}) }= q^{\frac{3}{10}}\\=\sqrt[10]{ q^{3} }\\---------------\)
8. \(\left(y^{\frac{-3}{5}}\right)^{\frac{5}{4}}\\= y^{ \frac{-3}{5} . \frac{5}{4} }= y^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ y^{3} }}=\frac{1}{\sqrt[4]{ y^{3} }}. \color{purple}{\frac{\sqrt[4]{ y }}{\sqrt[4]{ y }}} \\=\frac{\sqrt[4]{ y }}{|y|}\\---------------\)
9. \(\left(a^{\frac{1}{6}}\right)^{\frac{-2}{3}}\\= a^{ \frac{1}{6} . (\frac{-2}{3}) }= a^{\frac{-1}{9}}\\=\frac{1}{\sqrt[9]{ a }}=\frac{1}{\sqrt[9]{ a }}. \color{purple}{\frac{\sqrt[9]{ a^{8} }}{\sqrt[9]{ a^{8} }}} \\=\frac{\sqrt[9]{ a^{8} }}{a}\\---------------\)
10. \(\left(q^{\frac{-3}{2}}\right)^{\frac{5}{2}}\\= q^{ \frac{-3}{2} . \frac{5}{2} }= q^{\frac{-15}{4}}\\=\frac{1}{\sqrt[4]{ q^{15} }}\\=\frac{1}{|q^{3}|.\sqrt[4]{ q^{3} }}=\frac{1}{|q^{3}|.\sqrt[4]{ q^{3} }} \color{purple}{\frac{\sqrt[4]{ q }}{\sqrt[4]{ q }}} \\=\frac{\sqrt[4]{ q }}{|q^{4}|}\\---------------\)
11. \(\left(a^{\frac{-3}{2}}\right)^{-1}\\= a^{ \frac{-3}{2} . (-1) }= a^{\frac{3}{2}}\\= \sqrt{ a^{3} } =|a|. \sqrt{ a } \\---------------\)
12. \(\left(q^{2}\right)^{\frac{-3}{5}}\\= q^{ 2 . (\frac{-3}{5}) }= q^{\frac{-6}{5}}\\=\frac{1}{\sqrt[5]{ q^{6} }}\\=\frac{1}{q.\sqrt[5]{ q }}=\frac{1}{q.\sqrt[5]{ q }} \color{purple}{\frac{\sqrt[5]{ q^{4} }}{\sqrt[5]{ q^{4} }}} \\=\frac{\sqrt[5]{ q^{4} }}{q^{2}}\\---------------\)