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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(a^{1}\right)^{1}\\= a^{ 1 . 1 }= a^{1}\\\\---------------\)
2. \(\left(a^{\frac{1}{2}}\right)^{\frac{3}{2}}\\= a^{ \frac{1}{2} . \frac{3}{2} }= a^{\frac{3}{4}}\\=\sqrt[4]{ a^{3} }\\---------------\)
3. \(\left(x^{-1}\right)^{\frac{-1}{6}}\\= x^{ -1 . (\frac{-1}{6}) }= x^{\frac{1}{6}}\\=\sqrt[6]{ x }\\---------------\)
4. \(\left(x^{\frac{5}{6}}\right)^{\frac{-2}{3}}\\= x^{ \frac{5}{6} . (\frac{-2}{3}) }= x^{\frac{-5}{9}}\\=\frac{1}{\sqrt[9]{ x^{5} }}=\frac{1}{\sqrt[9]{ x^{5} }}. \color{purple}{\frac{\sqrt[9]{ x^{4} }}{\sqrt[9]{ x^{4} }}} \\=\frac{\sqrt[9]{ x^{4} }}{x}\\---------------\)
5. \(\left(y^{\frac{-1}{3}}\right)^{\frac{-1}{2}}\\= y^{ \frac{-1}{3} . (\frac{-1}{2}) }= y^{\frac{1}{6}}\\=\sqrt[6]{ y }\\---------------\)
6. \(\left(q^{\frac{3}{5}}\right)^{\frac{-2}{5}}\\= q^{ \frac{3}{5} . (\frac{-2}{5}) }= q^{\frac{-6}{25}}\\=\frac{1}{\sqrt[25]{ q^{6} }}=\frac{1}{\sqrt[25]{ q^{6} }}. \color{purple}{\frac{\sqrt[25]{ q^{19} }}{\sqrt[25]{ q^{19} }}} \\=\frac{\sqrt[25]{ q^{19} }}{q}\\---------------\)
7. \(\left(q^{\frac{-2}{3}}\right)^{\frac{1}{4}}\\= q^{ \frac{-2}{3} . \frac{1}{4} }= q^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ q }}=\frac{1}{\sqrt[6]{ q }}. \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q|}\\---------------\)
8. \(\left(q^{\frac{-2}{3}}\right)^{\frac{2}{5}}\\= q^{ \frac{-2}{3} . \frac{2}{5} }= q^{\frac{-4}{15}}\\=\frac{1}{\sqrt[15]{ q^{4} }}=\frac{1}{\sqrt[15]{ q^{4} }}. \color{purple}{\frac{\sqrt[15]{ q^{11} }}{\sqrt[15]{ q^{11} }}} \\=\frac{\sqrt[15]{ q^{11} }}{q}\\---------------\)
9. \(\left(y^{\frac{5}{2}}\right)^{\frac{4}{3}}\\= y^{ \frac{5}{2} . \frac{4}{3} }= y^{\frac{10}{3}}\\=\sqrt[3]{ y^{10} }=y^{3}.\sqrt[3]{ y }\\---------------\)
10. \(\left(y^{\frac{4}{5}}\right)^{\frac{-5}{2}}\\= y^{ \frac{4}{5} . (\frac{-5}{2}) }= y^{-2}\\=\frac{1}{y^{2}}\\---------------\)
11. \(\left(y^{\frac{-5}{3}}\right)^{1}\\= y^{ \frac{-5}{3} . 1 }= y^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ y^{5} }}\\=\frac{1}{y.\sqrt[3]{ y^{2} }}=\frac{1}{y.\sqrt[3]{ y^{2} }} \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y^{2}}\\---------------\)
12. \(\left(y^{\frac{1}{6}}\right)^{\frac{4}{3}}\\= y^{ \frac{1}{6} . \frac{4}{3} }= y^{\frac{2}{9}}\\=\sqrt[9]{ y^{2} }\\---------------\)