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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(q^{\frac{-5}{4}}\right)^{\frac{-4}{5}}\\= q^{ \frac{-5}{4} . (\frac{-4}{5}) }= q^{1}\\\\---------------\)
2. \(\left(a^{\frac{-1}{3}}\right)^{\frac{-3}{5}}\\= a^{ \frac{-1}{3} . (\frac{-3}{5}) }= a^{\frac{1}{5}}\\=\sqrt[5]{ a }\\---------------\)
3. \(\left(x^{1}\right)^{\frac{-1}{4}}\\= x^{ 1 . (\frac{-1}{4}) }= x^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ x }}=\frac{1}{\sqrt[4]{ x }}. \color{purple}{\frac{\sqrt[4]{ x^{3} }}{\sqrt[4]{ x^{3} }}} \\=\frac{\sqrt[4]{ x^{3} }}{|x|}\\---------------\)
4. \(\left(x^{\frac{3}{2}}\right)^{1}\\= x^{ \frac{3}{2} . 1 }= x^{\frac{3}{2}}\\= \sqrt{ x^{3} } =|x|. \sqrt{ x } \\---------------\)
5. \(\left(a^{\frac{-1}{2}}\right)^{1}\\= a^{ \frac{-1}{2} . 1 }= a^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ a } }=\frac{1}{ \sqrt{ a } }. \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a|}\\---------------\)
6. \(\left(x^{-1}\right)^{-1}\\= x^{ -1 . (-1) }= x^{1}\\\\---------------\)
7. \(\left(a^{\frac{-1}{6}}\right)^{\frac{-1}{6}}\\= a^{ \frac{-1}{6} . (\frac{-1}{6}) }= a^{\frac{1}{36}}\\=\sqrt[36]{ a }\\---------------\)
8. \(\left(x^{\frac{1}{3}}\right)^{\frac{-1}{4}}\\= x^{ \frac{1}{3} . (\frac{-1}{4}) }= x^{\frac{-1}{12}}\\=\frac{1}{\sqrt[12]{ x }}=\frac{1}{\sqrt[12]{ x }}. \color{purple}{\frac{\sqrt[12]{ x^{11} }}{\sqrt[12]{ x^{11} }}} \\=\frac{\sqrt[12]{ x^{11} }}{|x|}\\---------------\)
9. \(\left(q^{\frac{-5}{6}}\right)^{\frac{-1}{5}}\\= q^{ \frac{-5}{6} . (\frac{-1}{5}) }= q^{\frac{1}{6}}\\=\sqrt[6]{ q }\\---------------\)
10. \(\left(y^{\frac{2}{3}}\right)^{\frac{-1}{4}}\\= y^{ \frac{2}{3} . (\frac{-1}{4}) }= y^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ y }}=\frac{1}{\sqrt[6]{ y }}. \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y|}\\---------------\)
11. \(\left(x^{\frac{3}{5}}\right)^{1}\\= x^{ \frac{3}{5} . 1 }= x^{\frac{3}{5}}\\=\sqrt[5]{ x^{3} }\\---------------\)
12. \(\left(q^{\frac{-1}{2}}\right)^{\frac{4}{3}}\\= q^{ \frac{-1}{2} . \frac{4}{3} }= q^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ q^{2} }}=\frac{1}{\sqrt[3]{ q^{2} }}. \color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q}\\---------------\)