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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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