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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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