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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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