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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(q^{-1}\right)^{1}\\= q^{ -1 . 1 }= q^{-1}\\=\frac{1}{q}\\---------------\)
2. \(\left(q^{1}\right)^{-1}\\= q^{ 1 . (-1) }= q^{-1}\\=\frac{1}{q}\\---------------\)
3. \(\left(y^{\frac{5}{4}}\right)^{\frac{-3}{5}}\\= y^{ \frac{5}{4} . (\frac{-3}{5}) }= y^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ y^{3} }}=\frac{1}{\sqrt[4]{ y^{3} }}. \color{purple}{\frac{\sqrt[4]{ y }}{\sqrt[4]{ y }}} \\=\frac{\sqrt[4]{ y }}{|y|}\\---------------\)
4. \(\left(x^{\frac{-3}{5}}\right)^{\frac{-5}{6}}\\= x^{ \frac{-3}{5} . (\frac{-5}{6}) }= x^{\frac{1}{2}}\\= \sqrt{ x } \\---------------\)
5. \(\left(a^{-2}\right)^{\frac{1}{2}}\\= a^{ -2 . \frac{1}{2} }= a^{-1}\\=\frac{1}{a}\\---------------\)
6. \(\left(q^{\frac{-1}{2}}\right)^{\frac{5}{4}}\\= q^{ \frac{-1}{2} . \frac{5}{4} }= q^{\frac{-5}{8}}\\=\frac{1}{\sqrt[8]{ q^{5} }}=\frac{1}{\sqrt[8]{ q^{5} }}. \color{purple}{\frac{\sqrt[8]{ q^{3} }}{\sqrt[8]{ q^{3} }}} \\=\frac{\sqrt[8]{ q^{3} }}{|q|}\\---------------\)
7. \(\left(y^{\frac{1}{4}}\right)^{1}\\= y^{ \frac{1}{4} . 1 }= y^{\frac{1}{4}}\\=\sqrt[4]{ y }\\---------------\)
8. \(\left(x^{\frac{1}{6}}\right)^{\frac{-1}{5}}\\= x^{ \frac{1}{6} . (\frac{-1}{5}) }= x^{\frac{-1}{30}}\\=\frac{1}{\sqrt[30]{ x }}=\frac{1}{\sqrt[30]{ x }}. \color{purple}{\frac{\sqrt[30]{ x^{29} }}{\sqrt[30]{ x^{29} }}} \\=\frac{\sqrt[30]{ x^{29} }}{|x|}\\---------------\)
9. \(\left(a^{-2}\right)^{-1}\\= a^{ -2 . (-1) }= a^{2}\\\\---------------\)
10. \(\left(y^{\frac{-2}{5}}\right)^{\frac{-1}{6}}\\= y^{ \frac{-2}{5} . (\frac{-1}{6}) }= y^{\frac{1}{15}}\\=\sqrt[15]{ y }\\---------------\)
11. \(\left(q^{\frac{5}{4}}\right)^{\frac{-1}{3}}\\= q^{ \frac{5}{4} . (\frac{-1}{3}) }= q^{\frac{-5}{12}}\\=\frac{1}{\sqrt[12]{ q^{5} }}=\frac{1}{\sqrt[12]{ q^{5} }}. \color{purple}{\frac{\sqrt[12]{ q^{7} }}{\sqrt[12]{ q^{7} }}} \\=\frac{\sqrt[12]{ q^{7} }}{|q|}\\---------------\)
12. \(\left(x^{\frac{1}{2}}\right)^{\frac{-2}{5}}\\= x^{ \frac{1}{2} . (\frac{-2}{5}) }= x^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ x }}=\frac{1}{\sqrt[5]{ x }}. \color{purple}{\frac{\sqrt[5]{ x^{4} }}{\sqrt[5]{ x^{4} }}} \\=\frac{\sqrt[5]{ x^{4} }}{x}\\---------------\)