Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{-3}{5}}}{y^{\frac{2}{3}}}\\= y^{ \frac{-3}{5} - \frac{2}{3} }= y^{\frac{-19}{15}}\\=\frac{1}{\sqrt[15]{ y^{19} }}\\=\frac{1}{y.\sqrt[15]{ y^{4} }}=\frac{1}{y.\sqrt[15]{ y^{4} }} \color{purple}{\frac{\sqrt[15]{ y^{11} }}{\sqrt[15]{ y^{11} }}} \\=\frac{\sqrt[15]{ y^{11} }}{y^{2}}\\---------------\)
2. \(\dfrac{a^{\frac{-4}{3}}}{a^{-1}}\\= a^{ \frac{-4}{3} - (-1) }= a^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ a }}=\frac{1}{\sqrt[3]{ a }}. \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a}\\---------------\)
3. \(\dfrac{q^{\frac{-1}{6}}}{q^{1}}\\= q^{ \frac{-1}{6} - 1 }= q^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ q^{7} }}\\=\frac{1}{|q|.\sqrt[6]{ q }}=\frac{1}{|q|.\sqrt[6]{ q }} \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q^{2}|}\\---------------\)
4. \(\dfrac{a^{1}}{a^{1}}\\= a^{ 1 - 1 }= a^{0}\\=1\\---------------\)
5. \(\dfrac{q^{\frac{3}{5}}}{q^{\frac{1}{2}}}\\= q^{ \frac{3}{5} - \frac{1}{2} }= q^{\frac{1}{10}}\\=\sqrt[10]{ q }\\---------------\)
6. \(\dfrac{q^{\frac{2}{5}}}{q^{\frac{1}{4}}}\\= q^{ \frac{2}{5} - \frac{1}{4} }= q^{\frac{3}{20}}\\=\sqrt[20]{ q^{3} }\\---------------\)
7. \(\dfrac{q^{\frac{1}{4}}}{q^{\frac{-3}{2}}}\\= q^{ \frac{1}{4} - (\frac{-3}{2}) }= q^{\frac{7}{4}}\\=\sqrt[4]{ q^{7} }=|q|.\sqrt[4]{ q^{3} }\\---------------\)
8. \(\dfrac{a^{1}}{a^{\frac{5}{4}}}\\= a^{ 1 - \frac{5}{4} }= a^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ a }}=\frac{1}{\sqrt[4]{ a }}. \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a|}\\---------------\)
9. \(\dfrac{a^{\frac{5}{3}}}{a^{\frac{-5}{4}}}\\= a^{ \frac{5}{3} - (\frac{-5}{4}) }= a^{\frac{35}{12}}\\=\sqrt[12]{ a^{35} }=|a^{2}|.\sqrt[12]{ a^{11} }\\---------------\)
10. \(\dfrac{a^{\frac{5}{3}}}{a^{\frac{-5}{3}}}\\= a^{ \frac{5}{3} - (\frac{-5}{3}) }= a^{\frac{10}{3}}\\=\sqrt[3]{ a^{10} }=a^{3}.\sqrt[3]{ a }\\---------------\)
11. \(\dfrac{y^{\frac{-2}{3}}}{y^{\frac{-5}{3}}}\\= y^{ \frac{-2}{3} - (\frac{-5}{3}) }= y^{1}\\\\---------------\)
12. \(\dfrac{a^{\frac{-1}{2}}}{a^{\frac{2}{5}}}\\= a^{ \frac{-1}{2} - \frac{2}{5} }= a^{\frac{-9}{10}}\\=\frac{1}{\sqrt[10]{ a^{9} }}=\frac{1}{\sqrt[10]{ a^{9} }}. \color{purple}{\frac{\sqrt[10]{ a }}{\sqrt[10]{ a }}} \\=\frac{\sqrt[10]{ a }}{|a|}\\---------------\)