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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(q^{\frac{-2}{5}}\right)^{\frac{-3}{2}}\\= q^{ \frac{-2}{5} . (\frac{-3}{2}) }= q^{\frac{3}{5}}\\=\sqrt[5]{ q^{3} }\\---------------\)
2. \(\left(q^{-1}\right)^{\frac{5}{2}}\\= q^{ -1 . \frac{5}{2} }= q^{\frac{-5}{2}}\\=\frac{1}{ \sqrt{ q^{5} } }\\=\frac{1}{|q^{2}|. \sqrt{ q } }=\frac{1}{|q^{2}|. \sqrt{ q } } \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q^{3}|}\\---------------\)
3. \(\left(a^{\frac{-4}{3}}\right)^{-1}\\= a^{ \frac{-4}{3} . (-1) }= a^{\frac{4}{3}}\\=\sqrt[3]{ a^{4} }=a.\sqrt[3]{ a }\\---------------\)
4. \(\left(y^{-1}\right)^{\frac{2}{3}}\\= y^{ -1 . \frac{2}{3} }= y^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ y^{2} }}=\frac{1}{\sqrt[3]{ y^{2} }}. \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y}\\---------------\)
5. \(\left(y^{-1}\right)^{\frac{-2}{5}}\\= y^{ -1 . (\frac{-2}{5}) }= y^{\frac{2}{5}}\\=\sqrt[5]{ y^{2} }\\---------------\)
6. \(\left(y^{\frac{-1}{5}}\right)^{\frac{-3}{5}}\\= y^{ \frac{-1}{5} . (\frac{-3}{5}) }= y^{\frac{3}{25}}\\=\sqrt[25]{ y^{3} }\\---------------\)
7. \(\left(y^{\frac{3}{2}}\right)^{\frac{-5}{3}}\\= y^{ \frac{3}{2} . (\frac{-5}{3}) }= y^{\frac{-5}{2}}\\=\frac{1}{ \sqrt{ y^{5} } }\\=\frac{1}{|y^{2}|. \sqrt{ y } }=\frac{1}{|y^{2}|. \sqrt{ y } } \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y^{3}|}\\---------------\)
8. \(\left(y^{\frac{-4}{5}}\right)^{\frac{-2}{3}}\\= y^{ \frac{-4}{5} . (\frac{-2}{3}) }= y^{\frac{8}{15}}\\=\sqrt[15]{ y^{8} }\\---------------\)
9. \(\left(q^{\frac{-4}{5}}\right)^{\frac{-3}{2}}\\= q^{ \frac{-4}{5} . (\frac{-3}{2}) }= q^{\frac{6}{5}}\\=\sqrt[5]{ q^{6} }=q.\sqrt[5]{ q }\\---------------\)
10. \(\left(a^{\frac{5}{3}}\right)^{-2}\\= a^{ \frac{5}{3} . (-2) }= a^{\frac{-10}{3}}\\=\frac{1}{\sqrt[3]{ a^{10} }}\\=\frac{1}{a^{3}.\sqrt[3]{ a }}=\frac{1}{a^{3}.\sqrt[3]{ a }} \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a^{4}}\\---------------\)
11. \(\left(x^{1}\right)^{\frac{-5}{4}}\\= x^{ 1 . (\frac{-5}{4}) }= x^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ x^{5} }}\\=\frac{1}{|x|.\sqrt[4]{ x }}=\frac{1}{|x|.\sqrt[4]{ x }} \color{purple}{\frac{\sqrt[4]{ x^{3} }}{\sqrt[4]{ x^{3} }}} \\=\frac{\sqrt[4]{ x^{3} }}{|x^{2}|}\\---------------\)
12. \(\left(x^{\frac{4}{5}}\right)^{\frac{-1}{5}}\\= x^{ \frac{4}{5} . (\frac{-1}{5}) }= x^{\frac{-4}{25}}\\=\frac{1}{\sqrt[25]{ x^{4} }}=\frac{1}{\sqrt[25]{ x^{4} }}. \color{purple}{\frac{\sqrt[25]{ x^{21} }}{\sqrt[25]{ x^{21} }}} \\=\frac{\sqrt[25]{ x^{21} }}{x}\\---------------\)