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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(a^{\frac{4}{5}}\right)^{\frac{4}{3}}\\= a^{ \frac{4}{5} . \frac{4}{3} }= a^{\frac{16}{15}}\\=\sqrt[15]{ a^{16} }=a.\sqrt[15]{ a }\\---------------\)
2. \(\left(a^{2}\right)^{-1}\\= a^{ 2 . (-1) }= a^{-2}\\=\frac{1}{a^{2}}\\---------------\)
3. \(\left(x^{-1}\right)^{\frac{-1}{3}}\\= x^{ -1 . (\frac{-1}{3}) }= x^{\frac{1}{3}}\\=\sqrt[3]{ x }\\---------------\)
4. \(\left(y^{\frac{-1}{5}}\right)^{\frac{-1}{3}}\\= y^{ \frac{-1}{5} . (\frac{-1}{3}) }= y^{\frac{1}{15}}\\=\sqrt[15]{ y }\\---------------\)
5. \(\left(x^{\frac{3}{2}}\right)^{\frac{-1}{2}}\\= x^{ \frac{3}{2} . (\frac{-1}{2}) }= x^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ x^{3} }}=\frac{1}{\sqrt[4]{ x^{3} }}. \color{purple}{\frac{\sqrt[4]{ x }}{\sqrt[4]{ x }}} \\=\frac{\sqrt[4]{ x }}{|x|}\\---------------\)
6. \(\left(a^{\frac{-3}{4}}\right)^{\frac{5}{2}}\\= a^{ \frac{-3}{4} . \frac{5}{2} }= a^{\frac{-15}{8}}\\=\frac{1}{\sqrt[8]{ a^{15} }}\\=\frac{1}{|a|.\sqrt[8]{ a^{7} }}=\frac{1}{|a|.\sqrt[8]{ a^{7} }} \color{purple}{\frac{\sqrt[8]{ a }}{\sqrt[8]{ a }}} \\=\frac{\sqrt[8]{ a }}{|a^{2}|}\\---------------\)
7. \(\left(a^{\frac{3}{5}}\right)^{\frac{-5}{6}}\\= a^{ \frac{3}{5} . (\frac{-5}{6}) }= a^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ a } }=\frac{1}{ \sqrt{ a } }. \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a|}\\---------------\)
8. \(\left(y^{\frac{-5}{4}}\right)^{\frac{-1}{2}}\\= y^{ \frac{-5}{4} . (\frac{-1}{2}) }= y^{\frac{5}{8}}\\=\sqrt[8]{ y^{5} }\\---------------\)
9. \(\left(a^{\frac{5}{3}}\right)^{\frac{-3}{2}}\\= a^{ \frac{5}{3} . (\frac{-3}{2}) }= a^{\frac{-5}{2}}\\=\frac{1}{ \sqrt{ a^{5} } }\\=\frac{1}{|a^{2}|. \sqrt{ a } }=\frac{1}{|a^{2}|. \sqrt{ a } } \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a^{3}|}\\---------------\)
10. \(\left(q^{\frac{2}{3}}\right)^{\frac{-5}{2}}\\= q^{ \frac{2}{3} . (\frac{-5}{2}) }= q^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ q^{5} }}\\=\frac{1}{q.\sqrt[3]{ q^{2} }}=\frac{1}{q.\sqrt[3]{ q^{2} }} \color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q^{2}}\\---------------\)
11. \(\left(x^{1}\right)^{\frac{2}{3}}\\= x^{ 1 . \frac{2}{3} }= x^{\frac{2}{3}}\\=\sqrt[3]{ x^{2} }\\---------------\)
12. \(\left(y^{\frac{-3}{4}}\right)^{\frac{-5}{3}}\\= y^{ \frac{-3}{4} . (\frac{-5}{3}) }= y^{\frac{5}{4}}\\=\sqrt[4]{ y^{5} }=|y|.\sqrt[4]{ y }\\---------------\)