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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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