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Werk uit m.b.v. de rekenregels

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

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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. \(\left(x^{\frac{-4}{5}}\right)^{\frac{-4}{3}}\\= x^{ \frac{-4}{5} . (\frac{-4}{3}) }= x^{\frac{16}{15}}\\=\sqrt[15]{ x^{16} }=x.\sqrt[15]{ x }\\---------------\)
3. \(\left(q^{\frac{-5}{2}}\right)^{\frac{1}{3}}\\= q^{ \frac{-5}{2} . \frac{1}{3} }= q^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ q^{5} }}=\frac{1}{\sqrt[6]{ q^{5} }}. \color{purple}{\frac{\sqrt[6]{ q }}{\sqrt[6]{ q }}} \\=\frac{\sqrt[6]{ q }}{|q|}\\---------------\)
4. \(\left(y^{-2}\right)^{\frac{4}{3}}\\= y^{ -2 . \frac{4}{3} }= y^{\frac{-8}{3}}\\=\frac{1}{\sqrt[3]{ y^{8} }}\\=\frac{1}{y^{2}.\sqrt[3]{ y^{2} }}=\frac{1}{y^{2}.\sqrt[3]{ y^{2} }} \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y^{3}}\\---------------\)
5. \(\left(a^{\frac{-2}{3}}\right)^{\frac{-2}{3}}\\= a^{ \frac{-2}{3} . (\frac{-2}{3}) }= a^{\frac{4}{9}}\\=\sqrt[9]{ a^{4} }\\---------------\)
6. \(\left(q^{-2}\right)^{\frac{-3}{5}}\\= q^{ -2 . (\frac{-3}{5}) }= q^{\frac{6}{5}}\\=\sqrt[5]{ q^{6} }=q.\sqrt[5]{ q }\\---------------\)
7. \(\left(y^{\frac{-1}{2}}\right)^{\frac{1}{2}}\\= y^{ \frac{-1}{2} . \frac{1}{2} }= y^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ y }}=\frac{1}{\sqrt[4]{ y }}. \color{purple}{\frac{\sqrt[4]{ y^{3} }}{\sqrt[4]{ y^{3} }}} \\=\frac{\sqrt[4]{ y^{3} }}{|y|}\\---------------\)
8. \(\left(q^{\frac{-1}{3}}\right)^{\frac{1}{2}}\\= q^{ \frac{-1}{3} . \frac{1}{2} }= q^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ q }}=\frac{1}{\sqrt[6]{ q }}. \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q|}\\---------------\)
9. \(\left(q^{\frac{-1}{6}}\right)^{\frac{-2}{3}}\\= q^{ \frac{-1}{6} . (\frac{-2}{3}) }= q^{\frac{1}{9}}\\=\sqrt[9]{ q }\\---------------\)
10. \(\left(y^{\frac{1}{3}}\right)^{\frac{1}{5}}\\= y^{ \frac{1}{3} . \frac{1}{5} }= y^{\frac{1}{15}}\\=\sqrt[15]{ y }\\---------------\)
11. \(\left(y^{1}\right)^{\frac{-3}{4}}\\= y^{ 1 . (\frac{-3}{4}) }= y^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ y^{3} }}=\frac{1}{\sqrt[4]{ y^{3} }}. \color{purple}{\frac{\sqrt[4]{ y }}{\sqrt[4]{ y }}} \\=\frac{\sqrt[4]{ y }}{|y|}\\---------------\)
12. \(\left(x^{\frac{1}{2}}\right)^{\frac{-4}{3}}\\= x^{ \frac{1}{2} . (\frac{-4}{3}) }= x^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ x^{2} }}=\frac{1}{\sqrt[3]{ x^{2} }}. \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x}\\---------------\)