Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{5}{2}}}{x^{\frac{-4}{5}}}\\= x^{ \frac{5}{2} - (\frac{-4}{5}) }= x^{\frac{33}{10}}\\=\sqrt[10]{ x^{33} }=|x^{3}|.\sqrt[10]{ x^{3} }\\---------------\)
2. \(\dfrac{y^{\frac{1}{2}}}{y^{1}}\\= y^{ \frac{1}{2} - 1 }= y^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ y } }=\frac{1}{ \sqrt{ y } }. \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y|}\\---------------\)
3. \(\dfrac{y^{\frac{5}{4}}}{y^{\frac{-3}{4}}}\\= y^{ \frac{5}{4} - (\frac{-3}{4}) }= y^{2}\\\\---------------\)
4. \(\dfrac{y^{\frac{-5}{4}}}{y^{\frac{-5}{2}}}\\= y^{ \frac{-5}{4} - (\frac{-5}{2}) }= y^{\frac{5}{4}}\\=\sqrt[4]{ y^{5} }=|y|.\sqrt[4]{ y }\\---------------\)
5. \(\dfrac{x^{\frac{-1}{3}}}{x^{\frac{-5}{2}}}\\= x^{ \frac{-1}{3} - (\frac{-5}{2}) }= x^{\frac{13}{6}}\\=\sqrt[6]{ x^{13} }=|x^{2}|.\sqrt[6]{ x }\\---------------\)
6. \(\dfrac{x^{\frac{5}{6}}}{x^{\frac{-4}{3}}}\\= x^{ \frac{5}{6} - (\frac{-4}{3}) }= x^{\frac{13}{6}}\\=\sqrt[6]{ x^{13} }=|x^{2}|.\sqrt[6]{ x }\\---------------\)
7. \(\dfrac{a^{-1}}{a^{\frac{5}{3}}}\\= a^{ -1 - \frac{5}{3} }= a^{\frac{-8}{3}}\\=\frac{1}{\sqrt[3]{ a^{8} }}\\=\frac{1}{a^{2}.\sqrt[3]{ a^{2} }}=\frac{1}{a^{2}.\sqrt[3]{ a^{2} }} \color{purple}{\frac{\sqrt[3]{ a }}{\sqrt[3]{ a }}} \\=\frac{\sqrt[3]{ a }}{a^{3}}\\---------------\)
8. \(\dfrac{y^{\frac{1}{3}}}{y^{\frac{-1}{2}}}\\= y^{ \frac{1}{3} - (\frac{-1}{2}) }= y^{\frac{5}{6}}\\=\sqrt[6]{ y^{5} }\\---------------\)
9. \(\dfrac{q^{\frac{-1}{5}}}{q^{\frac{1}{3}}}\\= q^{ \frac{-1}{5} - \frac{1}{3} }= q^{\frac{-8}{15}}\\=\frac{1}{\sqrt[15]{ q^{8} }}=\frac{1}{\sqrt[15]{ q^{8} }}. \color{purple}{\frac{\sqrt[15]{ q^{7} }}{\sqrt[15]{ q^{7} }}} \\=\frac{\sqrt[15]{ q^{7} }}{q}\\---------------\)
10. \(\dfrac{q^{\frac{-1}{2}}}{q^{\frac{1}{2}}}\\= q^{ \frac{-1}{2} - \frac{1}{2} }= q^{-1}\\=\frac{1}{q}\\---------------\)
11. \(\dfrac{q^{1}}{q^{\frac{5}{4}}}\\= q^{ 1 - \frac{5}{4} }= q^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ q }}=\frac{1}{\sqrt[4]{ q }}. \color{purple}{\frac{\sqrt[4]{ q^{3} }}{\sqrt[4]{ q^{3} }}} \\=\frac{\sqrt[4]{ q^{3} }}{|q|}\\---------------\)
12. \(\dfrac{a^{\frac{4}{3}}}{a^{\frac{1}{3}}}\\= a^{ \frac{4}{3} - \frac{1}{3} }= a^{1}\\\\---------------\)