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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(q^{1}\right)^{\frac{-5}{3}}\\= q^{ 1 . (\frac{-5}{3}) }= q^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ q^{5} }}\\=\frac{1}{q.\sqrt[3]{ q^{2} }}=\frac{1}{q.\sqrt[3]{ q^{2} }} \color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q^{2}}\\---------------\)
2. \(\left(y^{\frac{3}{5}}\right)^{\frac{-4}{5}}\\= y^{ \frac{3}{5} . (\frac{-4}{5}) }= y^{\frac{-12}{25}}\\=\frac{1}{\sqrt[25]{ y^{12} }}=\frac{1}{\sqrt[25]{ y^{12} }}. \color{purple}{\frac{\sqrt[25]{ y^{13} }}{\sqrt[25]{ y^{13} }}} \\=\frac{\sqrt[25]{ y^{13} }}{y}\\---------------\)
3. \(\left(x^{\frac{2}{3}}\right)^{\frac{-3}{5}}\\= x^{ \frac{2}{3} . (\frac{-3}{5}) }= x^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ x^{2} }}=\frac{1}{\sqrt[5]{ x^{2} }}. \color{purple}{\frac{\sqrt[5]{ x^{3} }}{\sqrt[5]{ x^{3} }}} \\=\frac{\sqrt[5]{ x^{3} }}{x}\\---------------\)
4. \(\left(y^{\frac{-1}{3}}\right)^{\frac{-1}{3}}\\= y^{ \frac{-1}{3} . (\frac{-1}{3}) }= y^{\frac{1}{9}}\\=\sqrt[9]{ y }\\---------------\)
5. \(\left(x^{\frac{-3}{2}}\right)^{\frac{-2}{5}}\\= x^{ \frac{-3}{2} . (\frac{-2}{5}) }= x^{\frac{3}{5}}\\=\sqrt[5]{ x^{3} }\\---------------\)
6. \(\left(y^{\frac{-1}{2}}\right)^{\frac{5}{3}}\\= y^{ \frac{-1}{2} . \frac{5}{3} }= y^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ y^{5} }}=\frac{1}{\sqrt[6]{ y^{5} }}. \color{purple}{\frac{\sqrt[6]{ y }}{\sqrt[6]{ y }}} \\=\frac{\sqrt[6]{ y }}{|y|}\\---------------\)
7. \(\left(x^{\frac{1}{2}}\right)^{\frac{-5}{3}}\\= x^{ \frac{1}{2} . (\frac{-5}{3}) }= x^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ x^{5} }}=\frac{1}{\sqrt[6]{ x^{5} }}. \color{purple}{\frac{\sqrt[6]{ x }}{\sqrt[6]{ x }}} \\=\frac{\sqrt[6]{ x }}{|x|}\\---------------\)
8. \(\left(y^{\frac{-2}{5}}\right)^{-1}\\= y^{ \frac{-2}{5} . (-1) }= y^{\frac{2}{5}}\\=\sqrt[5]{ y^{2} }\\---------------\)
9. \(\left(x^{\frac{3}{5}}\right)^{2}\\= x^{ \frac{3}{5} . 2 }= x^{\frac{6}{5}}\\=\sqrt[5]{ x^{6} }=x.\sqrt[5]{ x }\\---------------\)
10. \(\left(q^{\frac{1}{4}}\right)^{\frac{-1}{6}}\\= q^{ \frac{1}{4} . (\frac{-1}{6}) }= q^{\frac{-1}{24}}\\=\frac{1}{\sqrt[24]{ q }}=\frac{1}{\sqrt[24]{ q }}. \color{purple}{\frac{\sqrt[24]{ q^{23} }}{\sqrt[24]{ q^{23} }}} \\=\frac{\sqrt[24]{ q^{23} }}{|q|}\\---------------\)
11. \(\left(x^{\frac{-1}{5}}\right)^{\frac{-5}{6}}\\= x^{ \frac{-1}{5} . (\frac{-5}{6}) }= x^{\frac{1}{6}}\\=\sqrt[6]{ x }\\---------------\)
12. \(\left(x^{\frac{-5}{3}}\right)^{\frac{1}{4}}\\= x^{ \frac{-5}{3} . \frac{1}{4} }= x^{\frac{-5}{12}}\\=\frac{1}{\sqrt[12]{ x^{5} }}=\frac{1}{\sqrt[12]{ x^{5} }}. \color{purple}{\frac{\sqrt[12]{ x^{7} }}{\sqrt[12]{ x^{7} }}} \\=\frac{\sqrt[12]{ x^{7} }}{|x|}\\---------------\)