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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(y^{-1}\right)^{\frac{-3}{5}}\\= y^{ -1 . (\frac{-3}{5}) }= y^{\frac{3}{5}}\\=\sqrt[5]{ y^{3} }\\---------------\)
2. \(\left(y^{\frac{-3}{2}}\right)^{1}\\= y^{ \frac{-3}{2} . 1 }= y^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ y^{3} } }\\=\frac{1}{|y|. \sqrt{ y } }=\frac{1}{|y|. \sqrt{ y } } \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y^{2}|}\\---------------\)
3. \(\left(y^{\frac{-1}{2}}\right)^{\frac{-5}{4}}\\= y^{ \frac{-1}{2} . (\frac{-5}{4}) }= y^{\frac{5}{8}}\\=\sqrt[8]{ y^{5} }\\---------------\)
4. \(\left(y^{\frac{3}{4}}\right)^{\frac{1}{5}}\\= y^{ \frac{3}{4} . \frac{1}{5} }= y^{\frac{3}{20}}\\=\sqrt[20]{ y^{3} }\\---------------\)
5. \(\left(x^{\frac{3}{4}}\right)^{\frac{-1}{3}}\\= x^{ \frac{3}{4} . (\frac{-1}{3}) }= x^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ x }}=\frac{1}{\sqrt[4]{ x }}. \color{purple}{\frac{\sqrt[4]{ x^{3} }}{\sqrt[4]{ x^{3} }}} \\=\frac{\sqrt[4]{ x^{3} }}{|x|}\\---------------\)
6. \(\left(y^{\frac{1}{3}}\right)^{2}\\= y^{ \frac{1}{3} . 2 }= y^{\frac{2}{3}}\\=\sqrt[3]{ y^{2} }\\---------------\)
7. \(\left(y^{2}\right)^{\frac{2}{3}}\\= y^{ 2 . \frac{2}{3} }= y^{\frac{4}{3}}\\=\sqrt[3]{ y^{4} }=y.\sqrt[3]{ y }\\---------------\)
8. \(\left(x^{\frac{5}{4}}\right)^{\frac{1}{2}}\\= x^{ \frac{5}{4} . \frac{1}{2} }= x^{\frac{5}{8}}\\=\sqrt[8]{ x^{5} }\\---------------\)
9. \(\left(q^{\frac{-1}{2}}\right)^{1}\\= q^{ \frac{-1}{2} . 1 }= q^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ q } }=\frac{1}{ \sqrt{ q } }. \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q|}\\---------------\)
10. \(\left(y^{\frac{-2}{3}}\right)^{\frac{-5}{4}}\\= y^{ \frac{-2}{3} . (\frac{-5}{4}) }= y^{\frac{5}{6}}\\=\sqrt[6]{ y^{5} }\\---------------\)
11. \(\left(q^{\frac{5}{3}}\right)^{2}\\= q^{ \frac{5}{3} . 2 }= q^{\frac{10}{3}}\\=\sqrt[3]{ q^{10} }=q^{3}.\sqrt[3]{ q }\\---------------\)
12. \(\left(a^{\frac{1}{4}}\right)^{\frac{5}{3}}\\= a^{ \frac{1}{4} . \frac{5}{3} }= a^{\frac{5}{12}}\\=\sqrt[12]{ a^{5} }\\---------------\)