Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{2}{3}}}{q^{\frac{-2}{3}}}\\= q^{ \frac{2}{3} - (\frac{-2}{3}) }= q^{\frac{4}{3}}\\=\sqrt[3]{ q^{4} }=q.\sqrt[3]{ q }\\---------------\)
2. \(\dfrac{y^{\frac{5}{2}}}{y^{\frac{1}{3}}}\\= y^{ \frac{5}{2} - \frac{1}{3} }= y^{\frac{13}{6}}\\=\sqrt[6]{ y^{13} }=|y^{2}|.\sqrt[6]{ y }\\---------------\)
3. \(\dfrac{y^{\frac{5}{4}}}{y^{1}}\\= y^{ \frac{5}{4} - 1 }= y^{\frac{1}{4}}\\=\sqrt[4]{ y }\\---------------\)
4. \(\dfrac{x^{\frac{-1}{2}}}{x^{1}}\\= x^{ \frac{-1}{2} - 1 }= x^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ x^{3} } }\\=\frac{1}{|x|. \sqrt{ x } }=\frac{1}{|x|. \sqrt{ x } } \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x^{2}|}\\---------------\)
5. \(\dfrac{q^{1}}{q^{\frac{5}{3}}}\\= q^{ 1 - \frac{5}{3} }= q^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ q^{2} }}=\frac{1}{\sqrt[3]{ q^{2} }}. \color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q}\\---------------\)
6. \(\dfrac{x^{\frac{-1}{2}}}{x^{\frac{5}{4}}}\\= x^{ \frac{-1}{2} - \frac{5}{4} }= x^{\frac{-7}{4}}\\=\frac{1}{\sqrt[4]{ x^{7} }}\\=\frac{1}{|x|.\sqrt[4]{ x^{3} }}=\frac{1}{|x|.\sqrt[4]{ x^{3} }} \color{purple}{\frac{\sqrt[4]{ x }}{\sqrt[4]{ x }}} \\=\frac{\sqrt[4]{ x }}{|x^{2}|}\\---------------\)
7. \(\dfrac{y^{\frac{2}{5}}}{y^{\frac{-1}{2}}}\\= y^{ \frac{2}{5} - (\frac{-1}{2}) }= y^{\frac{9}{10}}\\=\sqrt[10]{ y^{9} }\\---------------\)
8. \(\dfrac{x^{\frac{-4}{5}}}{x^{\frac{-1}{2}}}\\= x^{ \frac{-4}{5} - (\frac{-1}{2}) }= x^{\frac{-3}{10}}\\=\frac{1}{\sqrt[10]{ x^{3} }}=\frac{1}{\sqrt[10]{ x^{3} }}. \color{purple}{\frac{\sqrt[10]{ x^{7} }}{\sqrt[10]{ x^{7} }}} \\=\frac{\sqrt[10]{ x^{7} }}{|x|}\\---------------\)
9. \(\dfrac{y^{1}}{y^{\frac{-5}{4}}}\\= y^{ 1 - (\frac{-5}{4}) }= y^{\frac{9}{4}}\\=\sqrt[4]{ y^{9} }=|y^{2}|.\sqrt[4]{ y }\\---------------\)
10. \(\dfrac{x^{2}}{x^{\frac{1}{2}}}\\= x^{ 2 - \frac{1}{2} }= x^{\frac{3}{2}}\\= \sqrt{ x^{3} } =|x|. \sqrt{ x } \\---------------\)
11. \(\dfrac{a^{\frac{1}{2}}}{a^{\frac{-5}{4}}}\\= a^{ \frac{1}{2} - (\frac{-5}{4}) }= a^{\frac{7}{4}}\\=\sqrt[4]{ a^{7} }=|a|.\sqrt[4]{ a^{3} }\\---------------\)
12. \(\dfrac{a^{\frac{-3}{4}}}{a^{1}}\\= a^{ \frac{-3}{4} - 1 }= a^{\frac{-7}{4}}\\=\frac{1}{\sqrt[4]{ a^{7} }}\\=\frac{1}{|a|.\sqrt[4]{ a^{3} }}=\frac{1}{|a|.\sqrt[4]{ a^{3} }} \color{purple}{\frac{\sqrt[4]{ a }}{\sqrt[4]{ a }}} \\=\frac{\sqrt[4]{ a }}{|a^{2}|}\\---------------\)