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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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