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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(y^{\frac{1}{5}}\right)^{\frac{-5}{4}}\\= y^{ \frac{1}{5} . (\frac{-5}{4}) }= y^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ y }}=\frac{1}{\sqrt[4]{ y }}. \color{purple}{\frac{\sqrt[4]{ y^{3} }}{\sqrt[4]{ y^{3} }}} \\=\frac{\sqrt[4]{ y^{3} }}{|y|}\\---------------\)
2. \(\left(x^{\frac{-5}{4}}\right)^{\frac{-5}{2}}\\= x^{ \frac{-5}{4} . (\frac{-5}{2}) }= x^{\frac{25}{8}}\\=\sqrt[8]{ x^{25} }=|x^{3}|.\sqrt[8]{ x }\\---------------\)
3. \(\left(y^{\frac{4}{5}}\right)^{\frac{1}{2}}\\= y^{ \frac{4}{5} . \frac{1}{2} }= y^{\frac{2}{5}}\\=\sqrt[5]{ y^{2} }\\---------------\)
4. \(\left(q^{-1}\right)^{\frac{5}{3}}\\= q^{ -1 . \frac{5}{3} }= q^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ q^{5} }}\\=\frac{1}{q.\sqrt[3]{ q^{2} }}=\frac{1}{q.\sqrt[3]{ q^{2} }} \color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q^{2}}\\---------------\)
5. \(\left(y^{\frac{4}{3}}\right)^{1}\\= y^{ \frac{4}{3} . 1 }= y^{\frac{4}{3}}\\=\sqrt[3]{ y^{4} }=y.\sqrt[3]{ y }\\---------------\)
6. \(\left(a^{\frac{-1}{3}}\right)^{\frac{4}{5}}\\= a^{ \frac{-1}{3} . \frac{4}{5} }= a^{\frac{-4}{15}}\\=\frac{1}{\sqrt[15]{ a^{4} }}=\frac{1}{\sqrt[15]{ a^{4} }}. \color{purple}{\frac{\sqrt[15]{ a^{11} }}{\sqrt[15]{ a^{11} }}} \\=\frac{\sqrt[15]{ a^{11} }}{a}\\---------------\)
7. \(\left(q^{1}\right)^{\frac{5}{6}}\\= q^{ 1 . \frac{5}{6} }= q^{\frac{5}{6}}\\=\sqrt[6]{ q^{5} }\\---------------\)
8. \(\left(y^{\frac{5}{6}}\right)^{\frac{1}{6}}\\= y^{ \frac{5}{6} . \frac{1}{6} }= y^{\frac{5}{36}}\\=\sqrt[36]{ y^{5} }\\---------------\)
9. \(\left(x^{\frac{3}{4}}\right)^{\frac{-5}{2}}\\= x^{ \frac{3}{4} . (\frac{-5}{2}) }= x^{\frac{-15}{8}}\\=\frac{1}{\sqrt[8]{ x^{15} }}\\=\frac{1}{|x|.\sqrt[8]{ x^{7} }}=\frac{1}{|x|.\sqrt[8]{ x^{7} }} \color{purple}{\frac{\sqrt[8]{ x }}{\sqrt[8]{ x }}} \\=\frac{\sqrt[8]{ x }}{|x^{2}|}\\---------------\)
10. \(\left(y^{\frac{-5}{6}}\right)^{-1}\\= y^{ \frac{-5}{6} . (-1) }= y^{\frac{5}{6}}\\=\sqrt[6]{ y^{5} }\\---------------\)
11. \(\left(a^{\frac{-3}{5}}\right)^{\frac{5}{4}}\\= a^{ \frac{-3}{5} . \frac{5}{4} }= a^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ a^{3} }}=\frac{1}{\sqrt[4]{ a^{3} }}. \color{purple}{\frac{\sqrt[4]{ a }}{\sqrt[4]{ a }}} \\=\frac{\sqrt[4]{ a }}{|a|}\\---------------\)
12. \(\left(q^{\frac{-2}{5}}\right)^{\frac{1}{5}}\\= q^{ \frac{-2}{5} . \frac{1}{5} }= q^{\frac{-2}{25}}\\=\frac{1}{\sqrt[25]{ q^{2} }}=\frac{1}{\sqrt[25]{ q^{2} }}. \color{purple}{\frac{\sqrt[25]{ q^{23} }}{\sqrt[25]{ q^{23} }}} \\=\frac{\sqrt[25]{ q^{23} }}{q}\\---------------\)