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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(y^{\frac{4}{5}}\right)^{\frac{3}{5}}\\= y^{ \frac{4}{5} . \frac{3}{5} }= y^{\frac{12}{25}}\\=\sqrt[25]{ y^{12} }\\---------------\)
2. \(\left(a^{\frac{5}{2}}\right)^{\frac{-1}{4}}\\= a^{ \frac{5}{2} . (\frac{-1}{4}) }= a^{\frac{-5}{8}}\\=\frac{1}{\sqrt[8]{ a^{5} }}=\frac{1}{\sqrt[8]{ a^{5} }}. \color{purple}{\frac{\sqrt[8]{ a^{3} }}{\sqrt[8]{ a^{3} }}} \\=\frac{\sqrt[8]{ a^{3} }}{|a|}\\---------------\)
3. \(\left(q^{1}\right)^{\frac{4}{3}}\\= q^{ 1 . \frac{4}{3} }= q^{\frac{4}{3}}\\=\sqrt[3]{ q^{4} }=q.\sqrt[3]{ q }\\---------------\)
4. \(\left(q^{\frac{-1}{2}}\right)^{\frac{3}{4}}\\= q^{ \frac{-1}{2} . \frac{3}{4} }= q^{\frac{-3}{8}}\\=\frac{1}{\sqrt[8]{ q^{3} }}=\frac{1}{\sqrt[8]{ q^{3} }}. \color{purple}{\frac{\sqrt[8]{ q^{5} }}{\sqrt[8]{ q^{5} }}} \\=\frac{\sqrt[8]{ q^{5} }}{|q|}\\---------------\)
5. \(\left(x^{\frac{4}{5}}\right)^{\frac{4}{5}}\\= x^{ \frac{4}{5} . \frac{4}{5} }= x^{\frac{16}{25}}\\=\sqrt[25]{ x^{16} }\\---------------\)
6. \(\left(x^{\frac{-5}{4}}\right)^{-1}\\= x^{ \frac{-5}{4} . (-1) }= x^{\frac{5}{4}}\\=\sqrt[4]{ x^{5} }=|x|.\sqrt[4]{ x }\\---------------\)
7. \(\left(x^{\frac{2}{5}}\right)^{-1}\\= x^{ \frac{2}{5} . (-1) }= x^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ x^{2} }}=\frac{1}{\sqrt[5]{ x^{2} }}. \color{purple}{\frac{\sqrt[5]{ x^{3} }}{\sqrt[5]{ x^{3} }}} \\=\frac{\sqrt[5]{ x^{3} }}{x}\\---------------\)
8. \(\left(y^{\frac{-2}{5}}\right)^{\frac{-1}{2}}\\= y^{ \frac{-2}{5} . (\frac{-1}{2}) }= y^{\frac{1}{5}}\\=\sqrt[5]{ y }\\---------------\)
9. \(\left(y^{1}\right)^{\frac{-5}{3}}\\= y^{ 1 . (\frac{-5}{3}) }= y^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ y^{5} }}\\=\frac{1}{y.\sqrt[3]{ y^{2} }}=\frac{1}{y.\sqrt[3]{ y^{2} }} \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y^{2}}\\---------------\)
10. \(\left(q^{\frac{5}{3}}\right)^{\frac{-2}{3}}\\= q^{ \frac{5}{3} . (\frac{-2}{3}) }= q^{\frac{-10}{9}}\\=\frac{1}{\sqrt[9]{ q^{10} }}\\=\frac{1}{q.\sqrt[9]{ q }}=\frac{1}{q.\sqrt[9]{ q }} \color{purple}{\frac{\sqrt[9]{ q^{8} }}{\sqrt[9]{ q^{8} }}} \\=\frac{\sqrt[9]{ q^{8} }}{q^{2}}\\---------------\)
11. \(\left(x^{\frac{-1}{2}}\right)^{-1}\\= x^{ \frac{-1}{2} . (-1) }= x^{\frac{1}{2}}\\= \sqrt{ x } \\---------------\)
12. \(\left(x^{\frac{-3}{4}}\right)^{\frac{5}{3}}\\= x^{ \frac{-3}{4} . \frac{5}{3} }= x^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ x^{5} }}\\=\frac{1}{|x|.\sqrt[4]{ x }}=\frac{1}{|x|.\sqrt[4]{ x }} \color{purple}{\frac{\sqrt[4]{ x^{3} }}{\sqrt[4]{ x^{3} }}} \\=\frac{\sqrt[4]{ x^{3} }}{|x^{2}|}\\---------------\)