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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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