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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(y^{1}\right)^{1}\\= y^{ 1 . 1 }= y^{1}\\\\---------------\)
2. \(\left(x^{\frac{-1}{2}}\right)^{\frac{-4}{3}}\\= x^{ \frac{-1}{2} . (\frac{-4}{3}) }= x^{\frac{2}{3}}\\=\sqrt[3]{ x^{2} }\\---------------\)
3. \(\left(a^{\frac{-4}{5}}\right)^{\frac{-5}{3}}\\= a^{ \frac{-4}{5} . (\frac{-5}{3}) }= a^{\frac{4}{3}}\\=\sqrt[3]{ a^{4} }=a.\sqrt[3]{ a }\\---------------\)
4. \(\left(q^{\frac{1}{2}}\right)^{\frac{1}{3}}\\= q^{ \frac{1}{2} . \frac{1}{3} }= q^{\frac{1}{6}}\\=\sqrt[6]{ q }\\---------------\)
5. \(\left(q^{\frac{2}{3}}\right)^{\frac{-2}{5}}\\= q^{ \frac{2}{3} . (\frac{-2}{5}) }= q^{\frac{-4}{15}}\\=\frac{1}{\sqrt[15]{ q^{4} }}=\frac{1}{\sqrt[15]{ q^{4} }}. \color{purple}{\frac{\sqrt[15]{ q^{11} }}{\sqrt[15]{ q^{11} }}} \\=\frac{\sqrt[15]{ q^{11} }}{q}\\---------------\)
6. \(\left(y^{\frac{-5}{3}}\right)^{\frac{1}{2}}\\= y^{ \frac{-5}{3} . \frac{1}{2} }= y^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ y^{5} }}=\frac{1}{\sqrt[6]{ y^{5} }}. \color{purple}{\frac{\sqrt[6]{ y }}{\sqrt[6]{ y }}} \\=\frac{\sqrt[6]{ y }}{|y|}\\---------------\)
7. \(\left(q^{-2}\right)^{-2}\\= q^{ -2 . (-2) }= q^{4}\\\\---------------\)
8. \(\left(y^{\frac{5}{6}}\right)^{\frac{-5}{4}}\\= y^{ \frac{5}{6} . (\frac{-5}{4}) }= y^{\frac{-25}{24}}\\=\frac{1}{\sqrt[24]{ y^{25} }}\\=\frac{1}{|y|.\sqrt[24]{ y }}=\frac{1}{|y|.\sqrt[24]{ y }} \color{purple}{\frac{\sqrt[24]{ y^{23} }}{\sqrt[24]{ y^{23} }}} \\=\frac{\sqrt[24]{ y^{23} }}{|y^{2}|}\\---------------\)
9. \(\left(a^{\frac{1}{3}}\right)^{\frac{5}{6}}\\= a^{ \frac{1}{3} . \frac{5}{6} }= a^{\frac{5}{18}}\\=\sqrt[18]{ a^{5} }\\---------------\)
10. \(\left(a^{\frac{1}{6}}\right)^{\frac{-2}{3}}\\= a^{ \frac{1}{6} . (\frac{-2}{3}) }= a^{\frac{-1}{9}}\\=\frac{1}{\sqrt[9]{ a }}=\frac{1}{\sqrt[9]{ a }}. \color{purple}{\frac{\sqrt[9]{ a^{8} }}{\sqrt[9]{ a^{8} }}} \\=\frac{\sqrt[9]{ a^{8} }}{a}\\---------------\)
11. \(\left(y^{\frac{-4}{3}}\right)^{-1}\\= y^{ \frac{-4}{3} . (-1) }= y^{\frac{4}{3}}\\=\sqrt[3]{ y^{4} }=y.\sqrt[3]{ y }\\---------------\)
12. \(\left(y^{\frac{-3}{4}}\right)^{\frac{1}{2}}\\= y^{ \frac{-3}{4} . \frac{1}{2} }= y^{\frac{-3}{8}}\\=\frac{1}{\sqrt[8]{ y^{3} }}=\frac{1}{\sqrt[8]{ y^{3} }}. \color{purple}{\frac{\sqrt[8]{ y^{5} }}{\sqrt[8]{ y^{5} }}} \\=\frac{\sqrt[8]{ y^{5} }}{|y|}\\---------------\)