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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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