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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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