Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{1}}{y^{\frac{1}{5}}}\\= y^{ 1 - \frac{1}{5} }= y^{\frac{4}{5}}\\=\sqrt[5]{ y^{4} }\\---------------\)
2. \(\dfrac{y^{\frac{5}{3}}}{y^{\frac{-2}{3}}}\\= y^{ \frac{5}{3} - (\frac{-2}{3}) }= y^{\frac{7}{3}}\\=\sqrt[3]{ y^{7} }=y^{2}.\sqrt[3]{ y }\\---------------\)
3. \(\dfrac{q^{\frac{-2}{3}}}{q^{-1}}\\= q^{ \frac{-2}{3} - (-1) }= q^{\frac{1}{3}}\\=\sqrt[3]{ q }\\---------------\)
4. \(\dfrac{x^{\frac{2}{3}}}{x^{\frac{-3}{5}}}\\= x^{ \frac{2}{3} - (\frac{-3}{5}) }= x^{\frac{19}{15}}\\=\sqrt[15]{ x^{19} }=x.\sqrt[15]{ x^{4} }\\---------------\)
5. \(\dfrac{x^{1}}{x^{\frac{-1}{2}}}\\= x^{ 1 - (\frac{-1}{2}) }= x^{\frac{3}{2}}\\= \sqrt{ x^{3} } =|x|. \sqrt{ x } \\---------------\)
6. \(\dfrac{a^{-1}}{a^{\frac{-3}{4}}}\\= a^{ -1 - (\frac{-3}{4}) }= a^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ a }}=\frac{1}{\sqrt[4]{ a }}. \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a|}\\---------------\)
7. \(\dfrac{a^{\frac{1}{6}}}{a^{1}}\\= a^{ \frac{1}{6} - 1 }= a^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ a^{5} }}=\frac{1}{\sqrt[6]{ a^{5} }}. \color{purple}{\frac{\sqrt[6]{ a }}{\sqrt[6]{ a }}} \\=\frac{\sqrt[6]{ a }}{|a|}\\---------------\)
8. \(\dfrac{q^{\frac{3}{4}}}{q^{\frac{-1}{5}}}\\= q^{ \frac{3}{4} - (\frac{-1}{5}) }= q^{\frac{19}{20}}\\=\sqrt[20]{ q^{19} }\\---------------\)
9. \(\dfrac{x^{\frac{-1}{5}}}{x^{\frac{-5}{3}}}\\= x^{ \frac{-1}{5} - (\frac{-5}{3}) }= x^{\frac{22}{15}}\\=\sqrt[15]{ x^{22} }=x.\sqrt[15]{ x^{7} }\\---------------\)
10. \(\dfrac{a^{\frac{-1}{3}}}{a^{\frac{1}{2}}}\\= a^{ \frac{-1}{3} - \frac{1}{2} }= a^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ a^{5} }}=\frac{1}{\sqrt[6]{ a^{5} }}. \color{purple}{\frac{\sqrt[6]{ a }}{\sqrt[6]{ a }}} \\=\frac{\sqrt[6]{ a }}{|a|}\\---------------\)
11. \(\dfrac{y^{\frac{3}{5}}}{y^{-1}}\\= y^{ \frac{3}{5} - (-1) }= y^{\frac{8}{5}}\\=\sqrt[5]{ y^{8} }=y.\sqrt[5]{ y^{3} }\\---------------\)
12. \(\dfrac{q^{1}}{q^{\frac{2}{3}}}\\= q^{ 1 - \frac{2}{3} }= q^{\frac{1}{3}}\\=\sqrt[3]{ q }\\---------------\)