Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{-1}}{y^{\frac{-5}{4}}}\\= y^{ -1 - (\frac{-5}{4}) }= y^{\frac{1}{4}}\\=\sqrt[4]{ y }\\---------------\)
2. \(\dfrac{q^{-1}}{q^{\frac{1}{2}}}\\= q^{ -1 - \frac{1}{2} }= q^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ q^{3} } }\\=\frac{1}{|q|. \sqrt{ q } }=\frac{1}{|q|. \sqrt{ q } } \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q^{2}|}\\---------------\)
3. \(\dfrac{a^{-2}}{a^{\frac{-2}{3}}}\\= a^{ -2 - (\frac{-2}{3}) }= a^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ a^{4} }}\\=\frac{1}{a.\sqrt[3]{ a }}=\frac{1}{a.\sqrt[3]{ a }} \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a^{2}}\\---------------\)
4. \(\dfrac{q^{\frac{-3}{5}}}{q^{\frac{-1}{3}}}\\= q^{ \frac{-3}{5} - (\frac{-1}{3}) }= q^{\frac{-4}{15}}\\=\frac{1}{\sqrt[15]{ q^{4} }}=\frac{1}{\sqrt[15]{ q^{4} }}. \color{purple}{\frac{\sqrt[15]{ q^{11} }}{\sqrt[15]{ q^{11} }}} \\=\frac{\sqrt[15]{ q^{11} }}{q}\\---------------\)
5. \(\dfrac{y^{\frac{2}{3}}}{y^{\frac{-2}{5}}}\\= y^{ \frac{2}{3} - (\frac{-2}{5}) }= y^{\frac{16}{15}}\\=\sqrt[15]{ y^{16} }=y.\sqrt[15]{ y }\\---------------\)
6. \(\dfrac{x^{\frac{-1}{2}}}{x^{-1}}\\= x^{ \frac{-1}{2} - (-1) }= x^{\frac{1}{2}}\\= \sqrt{ x } \\---------------\)
7. \(\dfrac{x^{\frac{-1}{3}}}{x^{\frac{-2}{5}}}\\= x^{ \frac{-1}{3} - (\frac{-2}{5}) }= x^{\frac{1}{15}}\\=\sqrt[15]{ x }\\---------------\)
8. \(\dfrac{y^{1}}{y^{-1}}\\= y^{ 1 - (-1) }= y^{2}\\\\---------------\)
9. \(\dfrac{x^{\frac{1}{2}}}{x^{1}}\\= x^{ \frac{1}{2} - 1 }= x^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ x } }=\frac{1}{ \sqrt{ x } }. \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x|}\\---------------\)
10. \(\dfrac{a^{\frac{2}{5}}}{a^{\frac{-3}{5}}}\\= a^{ \frac{2}{5} - (\frac{-3}{5}) }= a^{1}\\\\---------------\)
11. \(\dfrac{a^{\frac{1}{3}}}{a^{\frac{-4}{5}}}\\= a^{ \frac{1}{3} - (\frac{-4}{5}) }= a^{\frac{17}{15}}\\=\sqrt[15]{ a^{17} }=a.\sqrt[15]{ a^{2} }\\---------------\)
12. \(\dfrac{y^{\frac{-4}{5}}}{y^{\frac{-3}{5}}}\\= y^{ \frac{-4}{5} - (\frac{-3}{5}) }= y^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ y }}=\frac{1}{\sqrt[5]{ y }}. \color{purple}{\frac{\sqrt[5]{ y^{4} }}{\sqrt[5]{ y^{4} }}} \\=\frac{\sqrt[5]{ y^{4} }}{y}\\---------------\)