Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{-2}{5}}}{y^{\frac{3}{5}}}\\= y^{ \frac{-2}{5} - \frac{3}{5} }= y^{-1}\\=\frac{1}{y}\\---------------\)
2. \(\dfrac{a^{\frac{3}{4}}}{a^{\frac{-1}{2}}}\\= a^{ \frac{3}{4} - (\frac{-1}{2}) }= a^{\frac{5}{4}}\\=\sqrt[4]{ a^{5} }=|a|.\sqrt[4]{ a }\\---------------\)
3. \(\dfrac{y^{\frac{-1}{3}}}{y^{\frac{-1}{5}}}\\= y^{ \frac{-1}{3} - (\frac{-1}{5}) }= y^{\frac{-2}{15}}\\=\frac{1}{\sqrt[15]{ y^{2} }}=\frac{1}{\sqrt[15]{ y^{2} }}. \color{purple}{\frac{\sqrt[15]{ y^{13} }}{\sqrt[15]{ y^{13} }}} \\=\frac{\sqrt[15]{ y^{13} }}{y}\\---------------\)
4. \(\dfrac{q^{-2}}{q^{\frac{5}{6}}}\\= q^{ -2 - \frac{5}{6} }= q^{\frac{-17}{6}}\\=\frac{1}{\sqrt[6]{ q^{17} }}\\=\frac{1}{|q^{2}|.\sqrt[6]{ q^{5} }}=\frac{1}{|q^{2}|.\sqrt[6]{ q^{5} }} \color{purple}{\frac{\sqrt[6]{ q }}{\sqrt[6]{ q }}} \\=\frac{\sqrt[6]{ q }}{|q^{3}|}\\---------------\)
5. \(\dfrac{y^{\frac{-1}{2}}}{y^{\frac{-2}{3}}}\\= y^{ \frac{-1}{2} - (\frac{-2}{3}) }= y^{\frac{1}{6}}\\=\sqrt[6]{ y }\\---------------\)
6. \(\dfrac{x^{-1}}{x^{\frac{-5}{3}}}\\= x^{ -1 - (\frac{-5}{3}) }= x^{\frac{2}{3}}\\=\sqrt[3]{ x^{2} }\\---------------\)
7. \(\dfrac{a^{\frac{-1}{3}}}{a^{\frac{2}{3}}}\\= a^{ \frac{-1}{3} - \frac{2}{3} }= a^{-1}\\=\frac{1}{a}\\---------------\)
8. \(\dfrac{q^{\frac{5}{4}}}{q^{\frac{-1}{5}}}\\= q^{ \frac{5}{4} - (\frac{-1}{5}) }= q^{\frac{29}{20}}\\=\sqrt[20]{ q^{29} }=|q|.\sqrt[20]{ q^{9} }\\---------------\)
9. \(\dfrac{y^{\frac{5}{2}}}{y^{\frac{1}{3}}}\\= y^{ \frac{5}{2} - \frac{1}{3} }= y^{\frac{13}{6}}\\=\sqrt[6]{ y^{13} }=|y^{2}|.\sqrt[6]{ y }\\---------------\)
10. \(\dfrac{y^{\frac{5}{3}}}{y^{\frac{-3}{5}}}\\= y^{ \frac{5}{3} - (\frac{-3}{5}) }= y^{\frac{34}{15}}\\=\sqrt[15]{ y^{34} }=y^{2}.\sqrt[15]{ y^{4} }\\---------------\)
11. \(\dfrac{a^{\frac{-1}{4}}}{a^{\frac{-1}{5}}}\\= a^{ \frac{-1}{4} - (\frac{-1}{5}) }= a^{\frac{-1}{20}}\\=\frac{1}{\sqrt[20]{ a }}=\frac{1}{\sqrt[20]{ a }}. \color{purple}{\frac{\sqrt[20]{ a^{19} }}{\sqrt[20]{ a^{19} }}} \\=\frac{\sqrt[20]{ a^{19} }}{|a|}\\---------------\)
12. \(\dfrac{y^{\frac{1}{2}}}{y^{1}}\\= y^{ \frac{1}{2} - 1 }= y^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ y } }=\frac{1}{ \sqrt{ y } }. \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y|}\\---------------\)