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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(q^{\frac{-3}{5}}\right)^{1}\\= q^{ \frac{-3}{5} . 1 }= q^{\frac{-3}{5}}\\=\frac{1}{\sqrt[5]{ q^{3} }}=\frac{1}{\sqrt[5]{ q^{3} }}. \color{purple}{\frac{\sqrt[5]{ q^{2} }}{\sqrt[5]{ q^{2} }}} \\=\frac{\sqrt[5]{ q^{2} }}{q}\\---------------\)
2. \(\left(a^{-1}\right)^{\frac{2}{5}}\\= a^{ -1 . \frac{2}{5} }= a^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ a^{2} }}=\frac{1}{\sqrt[5]{ a^{2} }}. \color{purple}{\frac{\sqrt[5]{ a^{3} }}{\sqrt[5]{ a^{3} }}} \\=\frac{\sqrt[5]{ a^{3} }}{a}\\---------------\)
3. \(\left(x^{\frac{-4}{3}}\right)^{\frac{-1}{2}}\\= x^{ \frac{-4}{3} . (\frac{-1}{2}) }= x^{\frac{2}{3}}\\=\sqrt[3]{ x^{2} }\\---------------\)
4. \(\left(a^{\frac{-3}{5}}\right)^{\frac{3}{5}}\\= a^{ \frac{-3}{5} . \frac{3}{5} }= a^{\frac{-9}{25}}\\=\frac{1}{\sqrt[25]{ a^{9} }}=\frac{1}{\sqrt[25]{ a^{9} }}. \color{purple}{\frac{\sqrt[25]{ a^{16} }}{\sqrt[25]{ a^{16} }}} \\=\frac{\sqrt[25]{ a^{16} }}{a}\\---------------\)
5. \(\left(a^{\frac{3}{5}}\right)^{1}\\= a^{ \frac{3}{5} . 1 }= a^{\frac{3}{5}}\\=\sqrt[5]{ a^{3} }\\---------------\)
6. \(\left(y^{\frac{1}{3}}\right)^{\frac{-2}{5}}\\= y^{ \frac{1}{3} . (\frac{-2}{5}) }= y^{\frac{-2}{15}}\\=\frac{1}{\sqrt[15]{ y^{2} }}=\frac{1}{\sqrt[15]{ y^{2} }}. \color{purple}{\frac{\sqrt[15]{ y^{13} }}{\sqrt[15]{ y^{13} }}} \\=\frac{\sqrt[15]{ y^{13} }}{y}\\---------------\)
7. \(\left(y^{-1}\right)^{\frac{-1}{5}}\\= y^{ -1 . (\frac{-1}{5}) }= y^{\frac{1}{5}}\\=\sqrt[5]{ y }\\---------------\)
8. \(\left(x^{\frac{1}{2}}\right)^{\frac{-3}{4}}\\= x^{ \frac{1}{2} . (\frac{-3}{4}) }= x^{\frac{-3}{8}}\\=\frac{1}{\sqrt[8]{ x^{3} }}=\frac{1}{\sqrt[8]{ x^{3} }}. \color{purple}{\frac{\sqrt[8]{ x^{5} }}{\sqrt[8]{ x^{5} }}} \\=\frac{\sqrt[8]{ x^{5} }}{|x|}\\---------------\)
9. \(\left(a^{\frac{2}{5}}\right)^{\frac{-2}{5}}\\= a^{ \frac{2}{5} . (\frac{-2}{5}) }= a^{\frac{-4}{25}}\\=\frac{1}{\sqrt[25]{ a^{4} }}=\frac{1}{\sqrt[25]{ a^{4} }}. \color{purple}{\frac{\sqrt[25]{ a^{21} }}{\sqrt[25]{ a^{21} }}} \\=\frac{\sqrt[25]{ a^{21} }}{a}\\---------------\)
10. \(\left(y^{\frac{3}{2}}\right)^{\frac{-1}{3}}\\= y^{ \frac{3}{2} . (\frac{-1}{3}) }= y^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ y } }=\frac{1}{ \sqrt{ y } }. \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y|}\\---------------\)
11. \(\left(y^{\frac{-1}{2}}\right)^{\frac{3}{4}}\\= y^{ \frac{-1}{2} . \frac{3}{4} }= y^{\frac{-3}{8}}\\=\frac{1}{\sqrt[8]{ y^{3} }}=\frac{1}{\sqrt[8]{ y^{3} }}. \color{purple}{\frac{\sqrt[8]{ y^{5} }}{\sqrt[8]{ y^{5} }}} \\=\frac{\sqrt[8]{ y^{5} }}{|y|}\\---------------\)
12. \(\left(x^{\frac{-1}{3}}\right)^{\frac{1}{2}}\\= x^{ \frac{-1}{3} . \frac{1}{2} }= x^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ x }}=\frac{1}{\sqrt[6]{ x }}. \color{purple}{\frac{\sqrt[6]{ x^{5} }}{\sqrt[6]{ x^{5} }}} \\=\frac{\sqrt[6]{ x^{5} }}{|x|}\\---------------\)