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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(q^{-2}\right)^{\frac{-4}{5}}\\= q^{ -2 . (\frac{-4}{5}) }= q^{\frac{8}{5}}\\=\sqrt[5]{ q^{8} }=q.\sqrt[5]{ q^{3} }\\---------------\)
2. \(\left(y^{\frac{1}{3}}\right)^{\frac{-3}{2}}\\= y^{ \frac{1}{3} . (\frac{-3}{2}) }= y^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ y } }=\frac{1}{ \sqrt{ y } }. \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y|}\\---------------\)
3. \(\left(y^{\frac{1}{5}}\right)^{\frac{3}{5}}\\= y^{ \frac{1}{5} . \frac{3}{5} }= y^{\frac{3}{25}}\\=\sqrt[25]{ y^{3} }\\---------------\)
4. \(\left(q^{\frac{2}{3}}\right)^{\frac{2}{3}}\\= q^{ \frac{2}{3} . \frac{2}{3} }= q^{\frac{4}{9}}\\=\sqrt[9]{ q^{4} }\\---------------\)
5. \(\left(a^{-1}\right)^{\frac{-2}{3}}\\= a^{ -1 . (\frac{-2}{3}) }= a^{\frac{2}{3}}\\=\sqrt[3]{ a^{2} }\\---------------\)
6. \(\left(y^{1}\right)^{\frac{1}{5}}\\= y^{ 1 . \frac{1}{5} }= y^{\frac{1}{5}}\\=\sqrt[5]{ y }\\---------------\)
7. \(\left(y^{\frac{-4}{5}}\right)^{\frac{4}{5}}\\= y^{ \frac{-4}{5} . \frac{4}{5} }= y^{\frac{-16}{25}}\\=\frac{1}{\sqrt[25]{ y^{16} }}=\frac{1}{\sqrt[25]{ y^{16} }}. \color{purple}{\frac{\sqrt[25]{ y^{9} }}{\sqrt[25]{ y^{9} }}} \\=\frac{\sqrt[25]{ y^{9} }}{y}\\---------------\)
8. \(\left(x^{\frac{2}{5}}\right)^{\frac{-4}{3}}\\= x^{ \frac{2}{5} . (\frac{-4}{3}) }= x^{\frac{-8}{15}}\\=\frac{1}{\sqrt[15]{ x^{8} }}=\frac{1}{\sqrt[15]{ x^{8} }}. \color{purple}{\frac{\sqrt[15]{ x^{7} }}{\sqrt[15]{ x^{7} }}} \\=\frac{\sqrt[15]{ x^{7} }}{x}\\---------------\)
9. \(\left(x^{\frac{3}{4}}\right)^{\frac{1}{3}}\\= x^{ \frac{3}{4} . \frac{1}{3} }= x^{\frac{1}{4}}\\=\sqrt[4]{ x }\\---------------\)
10. \(\left(y^{1}\right)^{\frac{5}{6}}\\= y^{ 1 . \frac{5}{6} }= y^{\frac{5}{6}}\\=\sqrt[6]{ y^{5} }\\---------------\)
11. \(\left(x^{\frac{5}{3}}\right)^{-1}\\= x^{ \frac{5}{3} . (-1) }= x^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ x^{5} }}\\=\frac{1}{x.\sqrt[3]{ x^{2} }}=\frac{1}{x.\sqrt[3]{ x^{2} }} \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x^{2}}\\---------------\)
12. \(\left(y^{\frac{1}{2}}\right)^{-1}\\= y^{ \frac{1}{2} . (-1) }= y^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ y } }=\frac{1}{ \sqrt{ y } }. \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y|}\\---------------\)