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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(y^{\frac{-3}{4}}\right)^{-1}\\= y^{ \frac{-3}{4} . (-1) }= y^{\frac{3}{4}}\\=\sqrt[4]{ y^{3} }\\---------------\)
2. \(\left(x^{\frac{-5}{2}}\right)^{\frac{-1}{5}}\\= x^{ \frac{-5}{2} . (\frac{-1}{5}) }= x^{\frac{1}{2}}\\= \sqrt{ x } \\---------------\)
3. \(\left(a^{\frac{5}{4}}\right)^{\frac{-5}{3}}\\= a^{ \frac{5}{4} . (\frac{-5}{3}) }= a^{\frac{-25}{12}}\\=\frac{1}{\sqrt[12]{ a^{25} }}\\=\frac{1}{|a^{2}|.\sqrt[12]{ a }}=\frac{1}{|a^{2}|.\sqrt[12]{ a }} \color{purple}{\frac{\sqrt[12]{ a^{11} }}{\sqrt[12]{ a^{11} }}} \\=\frac{\sqrt[12]{ a^{11} }}{|a^{3}|}\\---------------\)
4. \(\left(x^{\frac{4}{3}}\right)^{\frac{-2}{3}}\\= x^{ \frac{4}{3} . (\frac{-2}{3}) }= x^{\frac{-8}{9}}\\=\frac{1}{\sqrt[9]{ x^{8} }}=\frac{1}{\sqrt[9]{ x^{8} }}. \color{purple}{\frac{\sqrt[9]{ x }}{\sqrt[9]{ x }}} \\=\frac{\sqrt[9]{ x }}{x}\\---------------\)
5. \(\left(y^{\frac{-5}{2}}\right)^{-1}\\= y^{ \frac{-5}{2} . (-1) }= y^{\frac{5}{2}}\\= \sqrt{ y^{5} } =|y^{2}|. \sqrt{ y } \\---------------\)
6. \(\left(a^{-2}\right)^{\frac{-5}{3}}\\= a^{ -2 . (\frac{-5}{3}) }= a^{\frac{10}{3}}\\=\sqrt[3]{ a^{10} }=a^{3}.\sqrt[3]{ a }\\---------------\)
7. \(\left(q^{-1}\right)^{\frac{3}{5}}\\= q^{ -1 . \frac{3}{5} }= q^{\frac{-3}{5}}\\=\frac{1}{\sqrt[5]{ q^{3} }}=\frac{1}{\sqrt[5]{ q^{3} }}. \color{purple}{\frac{\sqrt[5]{ q^{2} }}{\sqrt[5]{ q^{2} }}} \\=\frac{\sqrt[5]{ q^{2} }}{q}\\---------------\)
8. \(\left(y^{\frac{3}{2}}\right)^{\frac{1}{3}}\\= y^{ \frac{3}{2} . \frac{1}{3} }= y^{\frac{1}{2}}\\= \sqrt{ y } \\---------------\)
9. \(\left(x^{\frac{2}{5}}\right)^{\frac{1}{2}}\\= x^{ \frac{2}{5} . \frac{1}{2} }= x^{\frac{1}{5}}\\=\sqrt[5]{ x }\\---------------\)
10. \(\left(q^{1}\right)^{1}\\= q^{ 1 . 1 }= q^{1}\\\\---------------\)
11. \(\left(x^{\frac{-3}{5}}\right)^{1}\\= x^{ \frac{-3}{5} . 1 }= x^{\frac{-3}{5}}\\=\frac{1}{\sqrt[5]{ x^{3} }}=\frac{1}{\sqrt[5]{ x^{3} }}. \color{purple}{\frac{\sqrt[5]{ x^{2} }}{\sqrt[5]{ x^{2} }}} \\=\frac{\sqrt[5]{ x^{2} }}{x}\\---------------\)
12. \(\left(y^{\frac{-5}{4}}\right)^{\frac{-1}{3}}\\= y^{ \frac{-5}{4} . (\frac{-1}{3}) }= y^{\frac{5}{12}}\\=\sqrt[12]{ y^{5} }\\---------------\)