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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(q^{\frac{-3}{4}}\right)^{\frac{-1}{4}}\\= q^{ \frac{-3}{4} . (\frac{-1}{4}) }= q^{\frac{3}{16}}\\=\sqrt[16]{ q^{3} }\\---------------\)
2. \(\left(q^{\frac{-2}{3}}\right)^{\frac{-3}{5}}\\= q^{ \frac{-2}{3} . (\frac{-3}{5}) }= q^{\frac{2}{5}}\\=\sqrt[5]{ q^{2} }\\---------------\)
3. \(\left(y^{\frac{1}{6}}\right)^{-1}\\= y^{ \frac{1}{6} . (-1) }= y^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ y }}=\frac{1}{\sqrt[6]{ y }}. \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y|}\\---------------\)
4. \(\left(q^{\frac{3}{5}}\right)^{\frac{1}{2}}\\= q^{ \frac{3}{5} . \frac{1}{2} }= q^{\frac{3}{10}}\\=\sqrt[10]{ q^{3} }\\---------------\)
5. \(\left(x^{\frac{-5}{3}}\right)^{1}\\= x^{ \frac{-5}{3} . 1 }= x^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ x^{5} }}\\=\frac{1}{x.\sqrt[3]{ x^{2} }}=\frac{1}{x.\sqrt[3]{ x^{2} }} \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x^{2}}\\---------------\)
6. \(\left(x^{\frac{-1}{2}}\right)^{\frac{1}{5}}\\= x^{ \frac{-1}{2} . \frac{1}{5} }= x^{\frac{-1}{10}}\\=\frac{1}{\sqrt[10]{ x }}=\frac{1}{\sqrt[10]{ x }}. \color{purple}{\frac{\sqrt[10]{ x^{9} }}{\sqrt[10]{ x^{9} }}} \\=\frac{\sqrt[10]{ x^{9} }}{|x|}\\---------------\)
7. \(\left(y^{-1}\right)^{\frac{-1}{3}}\\= y^{ -1 . (\frac{-1}{3}) }= y^{\frac{1}{3}}\\=\sqrt[3]{ y }\\---------------\)
8. \(\left(x^{\frac{-1}{2}}\right)^{\frac{-1}{2}}\\= x^{ \frac{-1}{2} . (\frac{-1}{2}) }= x^{\frac{1}{4}}\\=\sqrt[4]{ x }\\---------------\)
9. \(\left(q^{\frac{3}{4}}\right)^{\frac{4}{3}}\\= q^{ \frac{3}{4} . \frac{4}{3} }= q^{1}\\\\---------------\)
10. \(\left(q^{1}\right)^{1}\\= q^{ 1 . 1 }= q^{1}\\\\---------------\)
11. \(\left(q^{2}\right)^{\frac{3}{5}}\\= q^{ 2 . \frac{3}{5} }= q^{\frac{6}{5}}\\=\sqrt[5]{ q^{6} }=q.\sqrt[5]{ q }\\---------------\)
12. \(\left(y^{\frac{2}{3}}\right)^{1}\\= y^{ \frac{2}{3} . 1 }= y^{\frac{2}{3}}\\=\sqrt[3]{ y^{2} }\\---------------\)