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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(q^{\frac{-1}{6}}\right)^{\frac{-5}{4}}\\= q^{ \frac{-1}{6} . (\frac{-5}{4}) }= q^{\frac{5}{24}}\\=\sqrt[24]{ q^{5} }\\---------------\)
2. \(\left(q^{\frac{-5}{2}}\right)^{\frac{-1}{4}}\\= q^{ \frac{-5}{2} . (\frac{-1}{4}) }= q^{\frac{5}{8}}\\=\sqrt[8]{ q^{5} }\\---------------\)
3. \(\left(a^{\frac{-1}{5}}\right)^{\frac{-1}{2}}\\= a^{ \frac{-1}{5} . (\frac{-1}{2}) }= a^{\frac{1}{10}}\\=\sqrt[10]{ a }\\---------------\)
4. \(\left(a^{-1}\right)^{1}\\= a^{ -1 . 1 }= a^{-1}\\=\frac{1}{a}\\---------------\)
5. \(\left(q^{\frac{3}{2}}\right)^{\frac{1}{5}}\\= q^{ \frac{3}{2} . \frac{1}{5} }= q^{\frac{3}{10}}\\=\sqrt[10]{ q^{3} }\\---------------\)
6. \(\left(y^{\frac{1}{2}}\right)^{\frac{1}{3}}\\= y^{ \frac{1}{2} . \frac{1}{3} }= y^{\frac{1}{6}}\\=\sqrt[6]{ y }\\---------------\)
7. \(\left(q^{2}\right)^{\frac{-4}{3}}\\= q^{ 2 . (\frac{-4}{3}) }= q^{\frac{-8}{3}}\\=\frac{1}{\sqrt[3]{ q^{8} }}\\=\frac{1}{q^{2}.\sqrt[3]{ q^{2} }}=\frac{1}{q^{2}.\sqrt[3]{ q^{2} }} \color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q^{3}}\\---------------\)
8. \(\left(y^{\frac{-5}{2}}\right)^{\frac{5}{2}}\\= y^{ \frac{-5}{2} . \frac{5}{2} }= y^{\frac{-25}{4}}\\=\frac{1}{\sqrt[4]{ y^{25} }}\\=\frac{1}{|y^{6}|.\sqrt[4]{ y }}=\frac{1}{|y^{6}|.\sqrt[4]{ y }} \color{purple}{\frac{\sqrt[4]{ y^{3} }}{\sqrt[4]{ y^{3} }}} \\=\frac{\sqrt[4]{ y^{3} }}{|y^{7}|}\\---------------\)
9. \(\left(y^{\frac{-1}{3}}\right)^{1}\\= y^{ \frac{-1}{3} . 1 }= y^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ y }}=\frac{1}{\sqrt[3]{ y }}. \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y}\\---------------\)
10. \(\left(x^{\frac{5}{4}}\right)^{\frac{5}{3}}\\= x^{ \frac{5}{4} . \frac{5}{3} }= x^{\frac{25}{12}}\\=\sqrt[12]{ x^{25} }=|x^{2}|.\sqrt[12]{ x }\\---------------\)
11. \(\left(x^{\frac{-4}{5}}\right)^{\frac{-1}{5}}\\= x^{ \frac{-4}{5} . (\frac{-1}{5}) }= x^{\frac{4}{25}}\\=\sqrt[25]{ x^{4} }\\---------------\)
12. \(\left(a^{1}\right)^{1}\\= a^{ 1 . 1 }= a^{1}\\\\---------------\)