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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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