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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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