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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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