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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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