Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{-2}}{x^{\frac{1}{2}}}\\= x^{ -2 - \frac{1}{2} }= x^{\frac{-5}{2}}\\=\frac{1}{ \sqrt{ x^{5} } }\\=\frac{1}{|x^{2}|. \sqrt{ x } }=\frac{1}{|x^{2}|. \sqrt{ x } } \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x^{3}|}\\---------------\)
2. \(\dfrac{x^{-1}}{x^{-1}}\\= x^{ -1 - (-1) }= x^{0}\\=1\\---------------\)
3. \(\dfrac{y^{\frac{5}{4}}}{y^{\frac{-5}{2}}}\\= y^{ \frac{5}{4} - (\frac{-5}{2}) }= y^{\frac{15}{4}}\\=\sqrt[4]{ y^{15} }=|y^{3}|.\sqrt[4]{ y^{3} }\\---------------\)
4. \(\dfrac{q^{1}}{q^{\frac{-4}{5}}}\\= q^{ 1 - (\frac{-4}{5}) }= q^{\frac{9}{5}}\\=\sqrt[5]{ q^{9} }=q.\sqrt[5]{ q^{4} }\\---------------\)
5. \(\dfrac{y^{-1}}{y^{\frac{3}{2}}}\\= y^{ -1 - \frac{3}{2} }= y^{\frac{-5}{2}}\\=\frac{1}{ \sqrt{ y^{5} } }\\=\frac{1}{|y^{2}|. \sqrt{ y } }=\frac{1}{|y^{2}|. \sqrt{ y } } \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y^{3}|}\\---------------\)
6. \(\dfrac{a^{\frac{-1}{2}}}{a^{\frac{-2}{5}}}\\= a^{ \frac{-1}{2} - (\frac{-2}{5}) }= a^{\frac{-1}{10}}\\=\frac{1}{\sqrt[10]{ a }}=\frac{1}{\sqrt[10]{ a }}. \color{purple}{\frac{\sqrt[10]{ a^{9} }}{\sqrt[10]{ a^{9} }}} \\=\frac{\sqrt[10]{ a^{9} }}{|a|}\\---------------\)
7. \(\dfrac{a^{\frac{2}{3}}}{a^{\frac{2}{3}}}\\= a^{ \frac{2}{3} - \frac{2}{3} }= a^{0}\\=1\\---------------\)
8. \(\dfrac{x^{\frac{5}{3}}}{x^{\frac{-1}{4}}}\\= x^{ \frac{5}{3} - (\frac{-1}{4}) }= x^{\frac{23}{12}}\\=\sqrt[12]{ x^{23} }=|x|.\sqrt[12]{ x^{11} }\\---------------\)
9. \(\dfrac{y^{1}}{y^{\frac{1}{2}}}\\= y^{ 1 - \frac{1}{2} }= y^{\frac{1}{2}}\\= \sqrt{ y } \\---------------\)
10. \(\dfrac{y^{\frac{2}{3}}}{y^{1}}\\= y^{ \frac{2}{3} - 1 }= y^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ y }}=\frac{1}{\sqrt[3]{ y }}. \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y}\\---------------\)
11. \(\dfrac{a^{\frac{1}{2}}}{a^{\frac{-1}{6}}}\\= a^{ \frac{1}{2} - (\frac{-1}{6}) }= a^{\frac{2}{3}}\\=\sqrt[3]{ a^{2} }\\---------------\)
12. \(\dfrac{a^{\frac{3}{4}}}{a^{\frac{5}{2}}}\\= a^{ \frac{3}{4} - \frac{5}{2} }= a^{\frac{-7}{4}}\\=\frac{1}{\sqrt[4]{ a^{7} }}\\=\frac{1}{|a|.\sqrt[4]{ a^{3} }}=\frac{1}{|a|.\sqrt[4]{ a^{3} }} \color{purple}{\frac{\sqrt[4]{ a }}{\sqrt[4]{ a }}} \\=\frac{\sqrt[4]{ a }}{|a^{2}|}\\---------------\)