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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(q^{\frac{-4}{5}}\right)^{2}\\= q^{ \frac{-4}{5} . 2 }= q^{\frac{-8}{5}}\\=\frac{1}{\sqrt[5]{ q^{8} }}\\=\frac{1}{q.\sqrt[5]{ q^{3} }}=\frac{1}{q.\sqrt[5]{ q^{3} }} \color{purple}{\frac{\sqrt[5]{ q^{2} }}{\sqrt[5]{ q^{2} }}} \\=\frac{\sqrt[5]{ q^{2} }}{q^{2}}\\---------------\)
2. \(\left(q^{\frac{1}{5}}\right)^{\frac{-1}{3}}\\= q^{ \frac{1}{5} . (\frac{-1}{3}) }= q^{\frac{-1}{15}}\\=\frac{1}{\sqrt[15]{ q }}=\frac{1}{\sqrt[15]{ q }}. \color{purple}{\frac{\sqrt[15]{ q^{14} }}{\sqrt[15]{ q^{14} }}} \\=\frac{\sqrt[15]{ q^{14} }}{q}\\---------------\)
3. \(\left(y^{-1}\right)^{\frac{1}{2}}\\= y^{ -1 . \frac{1}{2} }= y^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ y } }=\frac{1}{ \sqrt{ y } }. \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y|}\\---------------\)
4. \(\left(q^{\frac{-1}{2}}\right)^{\frac{-1}{2}}\\= q^{ \frac{-1}{2} . (\frac{-1}{2}) }= q^{\frac{1}{4}}\\=\sqrt[4]{ q }\\---------------\)
5. \(\left(q^{\frac{2}{3}}\right)^{\frac{-2}{5}}\\= q^{ \frac{2}{3} . (\frac{-2}{5}) }= q^{\frac{-4}{15}}\\=\frac{1}{\sqrt[15]{ q^{4} }}=\frac{1}{\sqrt[15]{ q^{4} }}. \color{purple}{\frac{\sqrt[15]{ q^{11} }}{\sqrt[15]{ q^{11} }}} \\=\frac{\sqrt[15]{ q^{11} }}{q}\\---------------\)
6. \(\left(a^{-1}\right)^{\frac{3}{5}}\\= a^{ -1 . \frac{3}{5} }= a^{\frac{-3}{5}}\\=\frac{1}{\sqrt[5]{ a^{3} }}=\frac{1}{\sqrt[5]{ a^{3} }}. \color{purple}{\frac{\sqrt[5]{ a^{2} }}{\sqrt[5]{ a^{2} }}} \\=\frac{\sqrt[5]{ a^{2} }}{a}\\---------------\)
7. \(\left(q^{\frac{-5}{3}}\right)^{\frac{3}{5}}\\= q^{ \frac{-5}{3} . \frac{3}{5} }= q^{-1}\\=\frac{1}{q}\\---------------\)
8. \(\left(a^{-1}\right)^{\frac{4}{3}}\\= a^{ -1 . \frac{4}{3} }= a^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ a^{4} }}\\=\frac{1}{a.\sqrt[3]{ a }}=\frac{1}{a.\sqrt[3]{ a }} \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a^{2}}\\---------------\)
9. \(\left(y^{\frac{3}{4}}\right)^{\frac{2}{3}}\\= y^{ \frac{3}{4} . \frac{2}{3} }= y^{\frac{1}{2}}\\= \sqrt{ y } \\---------------\)
10. \(\left(y^{1}\right)^{\frac{-3}{2}}\\= y^{ 1 . (\frac{-3}{2}) }= y^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ y^{3} } }\\=\frac{1}{|y|. \sqrt{ y } }=\frac{1}{|y|. \sqrt{ y } } \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y^{2}|}\\---------------\)
11. \(\left(y^{1}\right)^{\frac{-1}{5}}\\= y^{ 1 . (\frac{-1}{5}) }= y^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ y }}=\frac{1}{\sqrt[5]{ y }}. \color{purple}{\frac{\sqrt[5]{ y^{4} }}{\sqrt[5]{ y^{4} }}} \\=\frac{\sqrt[5]{ y^{4} }}{y}\\---------------\)
12. \(\left(q^{\frac{3}{2}}\right)^{\frac{2}{3}}\\= q^{ \frac{3}{2} . \frac{2}{3} }= q^{1}\\\\---------------\)