Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{-2}{3}}}{q^{\frac{4}{5}}}\\= q^{ \frac{-2}{3} - \frac{4}{5} }= q^{\frac{-22}{15}}\\=\frac{1}{\sqrt[15]{ q^{22} }}\\=\frac{1}{q.\sqrt[15]{ q^{7} }}=\frac{1}{q.\sqrt[15]{ q^{7} }} \color{purple}{\frac{\sqrt[15]{ q^{8} }}{\sqrt[15]{ q^{8} }}} \\=\frac{\sqrt[15]{ q^{8} }}{q^{2}}\\---------------\)
2. \(\dfrac{q^{\frac{2}{3}}}{q^{\frac{5}{3}}}\\= q^{ \frac{2}{3} - \frac{5}{3} }= q^{-1}\\=\frac{1}{q}\\---------------\)
3. \(\dfrac{a^{\frac{-1}{4}}}{a^{\frac{1}{2}}}\\= a^{ \frac{-1}{4} - \frac{1}{2} }= a^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ a^{3} }}=\frac{1}{\sqrt[4]{ a^{3} }}. \color{purple}{\frac{\sqrt[4]{ a }}{\sqrt[4]{ a }}} \\=\frac{\sqrt[4]{ a }}{|a|}\\---------------\)
4. \(\dfrac{a^{\frac{1}{4}}}{a^{-2}}\\= a^{ \frac{1}{4} - (-2) }= a^{\frac{9}{4}}\\=\sqrt[4]{ a^{9} }=|a^{2}|.\sqrt[4]{ a }\\---------------\)
5. \(\dfrac{x^{\frac{5}{6}}}{x^{\frac{3}{5}}}\\= x^{ \frac{5}{6} - \frac{3}{5} }= x^{\frac{7}{30}}\\=\sqrt[30]{ x^{7} }\\---------------\)
6. \(\dfrac{x^{\frac{-2}{3}}}{x^{-2}}\\= x^{ \frac{-2}{3} - (-2) }= x^{\frac{4}{3}}\\=\sqrt[3]{ x^{4} }=x.\sqrt[3]{ x }\\---------------\)
7. \(\dfrac{x^{1}}{x^{\frac{-2}{3}}}\\= x^{ 1 - (\frac{-2}{3}) }= x^{\frac{5}{3}}\\=\sqrt[3]{ x^{5} }=x.\sqrt[3]{ x^{2} }\\---------------\)
8. \(\dfrac{q^{-2}}{q^{\frac{-5}{4}}}\\= q^{ -2 - (\frac{-5}{4}) }= q^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ q^{3} }}=\frac{1}{\sqrt[4]{ q^{3} }}. \color{purple}{\frac{\sqrt[4]{ q }}{\sqrt[4]{ q }}} \\=\frac{\sqrt[4]{ q }}{|q|}\\---------------\)
9. \(\dfrac{x^{\frac{-1}{2}}}{x^{\frac{3}{2}}}\\= x^{ \frac{-1}{2} - \frac{3}{2} }= x^{-2}\\=\frac{1}{x^{2}}\\---------------\)
10. \(\dfrac{y^{\frac{-5}{4}}}{y^{1}}\\= y^{ \frac{-5}{4} - 1 }= y^{\frac{-9}{4}}\\=\frac{1}{\sqrt[4]{ y^{9} }}\\=\frac{1}{|y^{2}|.\sqrt[4]{ y }}=\frac{1}{|y^{2}|.\sqrt[4]{ y }} \color{purple}{\frac{\sqrt[4]{ y^{3} }}{\sqrt[4]{ y^{3} }}} \\=\frac{\sqrt[4]{ y^{3} }}{|y^{3}|}\\---------------\)
11. \(\dfrac{a^{\frac{1}{2}}}{a^{\frac{3}{2}}}\\= a^{ \frac{1}{2} - \frac{3}{2} }= a^{-1}\\=\frac{1}{a}\\---------------\)
12. \(\dfrac{y^{\frac{1}{2}}}{y^{1}}\\= y^{ \frac{1}{2} - 1 }= y^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ y } }=\frac{1}{ \sqrt{ y } }. \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y|}\\---------------\)