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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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