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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(y^{\frac{5}{3}}\right)^{1}\\= y^{ \frac{5}{3} . 1 }= y^{\frac{5}{3}}\\=\sqrt[3]{ y^{5} }=y.\sqrt[3]{ y^{2} }\\---------------\)
2. \(\left(q^{\frac{4}{5}}\right)^{\frac{-2}{3}}\\= q^{ \frac{4}{5} . (\frac{-2}{3}) }= q^{\frac{-8}{15}}\\=\frac{1}{\sqrt[15]{ q^{8} }}=\frac{1}{\sqrt[15]{ q^{8} }}. \color{purple}{\frac{\sqrt[15]{ q^{7} }}{\sqrt[15]{ q^{7} }}} \\=\frac{\sqrt[15]{ q^{7} }}{q}\\---------------\)
3. \(\left(y^{\frac{3}{4}}\right)^{\frac{-3}{5}}\\= y^{ \frac{3}{4} . (\frac{-3}{5}) }= y^{\frac{-9}{20}}\\=\frac{1}{\sqrt[20]{ y^{9} }}=\frac{1}{\sqrt[20]{ y^{9} }}. \color{purple}{\frac{\sqrt[20]{ y^{11} }}{\sqrt[20]{ y^{11} }}} \\=\frac{\sqrt[20]{ y^{11} }}{|y|}\\---------------\)
4. \(\left(y^{\frac{-1}{2}}\right)^{\frac{-4}{3}}\\= y^{ \frac{-1}{2} . (\frac{-4}{3}) }= y^{\frac{2}{3}}\\=\sqrt[3]{ y^{2} }\\---------------\)
5. \(\left(y^{-1}\right)^{-1}\\= y^{ -1 . (-1) }= y^{1}\\\\---------------\)
6. \(\left(x^{\frac{-1}{5}}\right)^{\frac{-2}{3}}\\= x^{ \frac{-1}{5} . (\frac{-2}{3}) }= x^{\frac{2}{15}}\\=\sqrt[15]{ x^{2} }\\---------------\)
7. \(\left(a^{-1}\right)^{\frac{3}{4}}\\= a^{ -1 . \frac{3}{4} }= a^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ a^{3} }}=\frac{1}{\sqrt[4]{ a^{3} }}. \color{purple}{\frac{\sqrt[4]{ a }}{\sqrt[4]{ a }}} \\=\frac{\sqrt[4]{ a }}{|a|}\\---------------\)
8. \(\left(y^{\frac{-3}{2}}\right)^{-1}\\= y^{ \frac{-3}{2} . (-1) }= y^{\frac{3}{2}}\\= \sqrt{ y^{3} } =|y|. \sqrt{ y } \\---------------\)
9. \(\left(y^{2}\right)^{\frac{-3}{4}}\\= y^{ 2 . (\frac{-3}{4}) }= y^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ y^{3} } }\\=\frac{1}{|y|. \sqrt{ y } }=\frac{1}{|y|. \sqrt{ y } } \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y^{2}|}\\---------------\)
10. \(\left(a^{\frac{2}{3}}\right)^{\frac{-3}{2}}\\= a^{ \frac{2}{3} . (\frac{-3}{2}) }= a^{-1}\\=\frac{1}{a}\\---------------\)
11. \(\left(a^{\frac{1}{2}}\right)^{\frac{-1}{3}}\\= a^{ \frac{1}{2} . (\frac{-1}{3}) }= a^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ a }}=\frac{1}{\sqrt[6]{ a }}. \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a|}\\---------------\)
12. \(\left(x^{\frac{-5}{3}}\right)^{\frac{-1}{3}}\\= x^{ \frac{-5}{3} . (\frac{-1}{3}) }= x^{\frac{5}{9}}\\=\sqrt[9]{ x^{5} }\\---------------\)