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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(a^{\frac{-5}{2}}\right)^{\frac{2}{3}}\\= a^{ \frac{-5}{2} . \frac{2}{3} }= a^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ a^{5} }}\\=\frac{1}{a.\sqrt[3]{ a^{2} }}=\frac{1}{a.\sqrt[3]{ a^{2} }} \color{purple}{\frac{\sqrt[3]{ a }}{\sqrt[3]{ a }}} \\=\frac{\sqrt[3]{ a }}{a^{2}}\\---------------\)
2. \(\left(q^{\frac{5}{6}}\right)^{\frac{2}{3}}\\= q^{ \frac{5}{6} . \frac{2}{3} }= q^{\frac{5}{9}}\\=\sqrt[9]{ q^{5} }\\---------------\)
3. \(\left(x^{\frac{-3}{4}}\right)^{\frac{5}{2}}\\= x^{ \frac{-3}{4} . \frac{5}{2} }= x^{\frac{-15}{8}}\\=\frac{1}{\sqrt[8]{ x^{15} }}\\=\frac{1}{|x|.\sqrt[8]{ x^{7} }}=\frac{1}{|x|.\sqrt[8]{ x^{7} }} \color{purple}{\frac{\sqrt[8]{ x }}{\sqrt[8]{ x }}} \\=\frac{\sqrt[8]{ x }}{|x^{2}|}\\---------------\)
4. \(\left(x^{\frac{1}{2}}\right)^{\frac{-5}{6}}\\= x^{ \frac{1}{2} . (\frac{-5}{6}) }= x^{\frac{-5}{12}}\\=\frac{1}{\sqrt[12]{ x^{5} }}=\frac{1}{\sqrt[12]{ x^{5} }}. \color{purple}{\frac{\sqrt[12]{ x^{7} }}{\sqrt[12]{ x^{7} }}} \\=\frac{\sqrt[12]{ x^{7} }}{|x|}\\---------------\)
5. \(\left(x^{\frac{3}{5}}\right)^{\frac{-1}{6}}\\= x^{ \frac{3}{5} . (\frac{-1}{6}) }= x^{\frac{-1}{10}}\\=\frac{1}{\sqrt[10]{ x }}=\frac{1}{\sqrt[10]{ x }}. \color{purple}{\frac{\sqrt[10]{ x^{9} }}{\sqrt[10]{ x^{9} }}} \\=\frac{\sqrt[10]{ x^{9} }}{|x|}\\---------------\)
6. \(\left(x^{\frac{4}{3}}\right)^{\frac{-3}{2}}\\= x^{ \frac{4}{3} . (\frac{-3}{2}) }= x^{-2}\\=\frac{1}{x^{2}}\\---------------\)
7. \(\left(a^{\frac{3}{5}}\right)^{-1}\\= a^{ \frac{3}{5} . (-1) }= a^{\frac{-3}{5}}\\=\frac{1}{\sqrt[5]{ a^{3} }}=\frac{1}{\sqrt[5]{ a^{3} }}. \color{purple}{\frac{\sqrt[5]{ a^{2} }}{\sqrt[5]{ a^{2} }}} \\=\frac{\sqrt[5]{ a^{2} }}{a}\\---------------\)
8. \(\left(y^{\frac{1}{2}}\right)^{\frac{-1}{5}}\\= y^{ \frac{1}{2} . (\frac{-1}{5}) }= y^{\frac{-1}{10}}\\=\frac{1}{\sqrt[10]{ y }}=\frac{1}{\sqrt[10]{ y }}. \color{purple}{\frac{\sqrt[10]{ y^{9} }}{\sqrt[10]{ y^{9} }}} \\=\frac{\sqrt[10]{ y^{9} }}{|y|}\\---------------\)
9. \(\left(y^{\frac{-1}{4}}\right)^{\frac{2}{3}}\\= y^{ \frac{-1}{4} . \frac{2}{3} }= y^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ y }}=\frac{1}{\sqrt[6]{ y }}. \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y|}\\---------------\)
10. \(\left(q^{\frac{-4}{5}}\right)^{\frac{-5}{3}}\\= q^{ \frac{-4}{5} . (\frac{-5}{3}) }= q^{\frac{4}{3}}\\=\sqrt[3]{ q^{4} }=q.\sqrt[3]{ q }\\---------------\)
11. \(\left(q^{\frac{-1}{3}}\right)^{\frac{1}{3}}\\= q^{ \frac{-1}{3} . \frac{1}{3} }= q^{\frac{-1}{9}}\\=\frac{1}{\sqrt[9]{ q }}=\frac{1}{\sqrt[9]{ q }}. \color{purple}{\frac{\sqrt[9]{ q^{8} }}{\sqrt[9]{ q^{8} }}} \\=\frac{\sqrt[9]{ q^{8} }}{q}\\---------------\)
12. \(\left(q^{1}\right)^{\frac{2}{5}}\\= q^{ 1 . \frac{2}{5} }= q^{\frac{2}{5}}\\=\sqrt[5]{ q^{2} }\\---------------\)