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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(a^{-1}\right)^{\frac{-4}{3}}\\= a^{ -1 . (\frac{-4}{3}) }= a^{\frac{4}{3}}\\=\sqrt[3]{ a^{4} }=a.\sqrt[3]{ a }\\---------------\)
2. \(\left(y^{\frac{-1}{3}}\right)^{\frac{3}{2}}\\= y^{ \frac{-1}{3} . \frac{3}{2} }= y^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ y } }=\frac{1}{ \sqrt{ y } }. \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y|}\\---------------\)
3. \(\left(y^{\frac{-3}{5}}\right)^{\frac{3}{4}}\\= y^{ \frac{-3}{5} . \frac{3}{4} }= y^{\frac{-9}{20}}\\=\frac{1}{\sqrt[20]{ y^{9} }}=\frac{1}{\sqrt[20]{ y^{9} }}. \color{purple}{\frac{\sqrt[20]{ y^{11} }}{\sqrt[20]{ y^{11} }}} \\=\frac{\sqrt[20]{ y^{11} }}{|y|}\\---------------\)
4. \(\left(x^{\frac{-5}{6}}\right)^{\frac{1}{2}}\\= x^{ \frac{-5}{6} . \frac{1}{2} }= x^{\frac{-5}{12}}\\=\frac{1}{\sqrt[12]{ x^{5} }}=\frac{1}{\sqrt[12]{ x^{5} }}. \color{purple}{\frac{\sqrt[12]{ x^{7} }}{\sqrt[12]{ x^{7} }}} \\=\frac{\sqrt[12]{ x^{7} }}{|x|}\\---------------\)
5. \(\left(x^{2}\right)^{\frac{-1}{2}}\\= x^{ 2 . (\frac{-1}{2}) }= x^{-1}\\=\frac{1}{x}\\---------------\)
6. \(\left(a^{2}\right)^{\frac{-1}{5}}\\= a^{ 2 . (\frac{-1}{5}) }= a^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ a^{2} }}=\frac{1}{\sqrt[5]{ a^{2} }}. \color{purple}{\frac{\sqrt[5]{ a^{3} }}{\sqrt[5]{ a^{3} }}} \\=\frac{\sqrt[5]{ a^{3} }}{a}\\---------------\)
7. \(\left(x^{1}\right)^{\frac{-2}{5}}\\= x^{ 1 . (\frac{-2}{5}) }= x^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ x^{2} }}=\frac{1}{\sqrt[5]{ x^{2} }}. \color{purple}{\frac{\sqrt[5]{ x^{3} }}{\sqrt[5]{ x^{3} }}} \\=\frac{\sqrt[5]{ x^{3} }}{x}\\---------------\)
8. \(\left(q^{\frac{2}{3}}\right)^{\frac{-1}{2}}\\= q^{ \frac{2}{3} . (\frac{-1}{2}) }= q^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ q }}=\frac{1}{\sqrt[3]{ q }}. \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q}\\---------------\)
9. \(\left(y^{\frac{-4}{3}}\right)^{\frac{-1}{3}}\\= y^{ \frac{-4}{3} . (\frac{-1}{3}) }= y^{\frac{4}{9}}\\=\sqrt[9]{ y^{4} }\\---------------\)
10. \(\left(x^{\frac{-2}{5}}\right)^{\frac{4}{5}}\\= x^{ \frac{-2}{5} . \frac{4}{5} }= x^{\frac{-8}{25}}\\=\frac{1}{\sqrt[25]{ x^{8} }}=\frac{1}{\sqrt[25]{ x^{8} }}. \color{purple}{\frac{\sqrt[25]{ x^{17} }}{\sqrt[25]{ x^{17} }}} \\=\frac{\sqrt[25]{ x^{17} }}{x}\\---------------\)
11. \(\left(y^{\frac{-3}{4}}\right)^{\frac{-5}{6}}\\= y^{ \frac{-3}{4} . (\frac{-5}{6}) }= y^{\frac{5}{8}}\\=\sqrt[8]{ y^{5} }\\---------------\)
12. \(\left(x^{\frac{-4}{3}}\right)^{\frac{1}{2}}\\= x^{ \frac{-4}{3} . \frac{1}{2} }= x^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ x^{2} }}=\frac{1}{\sqrt[3]{ x^{2} }}. \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x}\\---------------\)