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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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