Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{1}}{y^{\frac{-3}{2}}}\\= y^{ 1 - (\frac{-3}{2}) }= y^{\frac{5}{2}}\\= \sqrt{ y^{5} } =|y^{2}|. \sqrt{ y } \\---------------\)
2. \(\dfrac{y^{\frac{1}{4}}}{y^{\frac{-2}{5}}}\\= y^{ \frac{1}{4} - (\frac{-2}{5}) }= y^{\frac{13}{20}}\\=\sqrt[20]{ y^{13} }\\---------------\)
3. \(\dfrac{x^{\frac{-1}{4}}}{x^{\frac{-1}{2}}}\\= x^{ \frac{-1}{4} - (\frac{-1}{2}) }= x^{\frac{1}{4}}\\=\sqrt[4]{ x }\\---------------\)
4. \(\dfrac{a^{\frac{-1}{4}}}{a^{\frac{-1}{6}}}\\= a^{ \frac{-1}{4} - (\frac{-1}{6}) }= a^{\frac{-1}{12}}\\=\frac{1}{\sqrt[12]{ a }}=\frac{1}{\sqrt[12]{ a }}. \color{purple}{\frac{\sqrt[12]{ a^{11} }}{\sqrt[12]{ a^{11} }}} \\=\frac{\sqrt[12]{ a^{11} }}{|a|}\\---------------\)
5. \(\dfrac{a^{\frac{-1}{2}}}{a^{\frac{-3}{5}}}\\= a^{ \frac{-1}{2} - (\frac{-3}{5}) }= a^{\frac{1}{10}}\\=\sqrt[10]{ a }\\---------------\)
6. \(\dfrac{x^{\frac{-5}{3}}}{x^{\frac{1}{5}}}\\= x^{ \frac{-5}{3} - \frac{1}{5} }= x^{\frac{-28}{15}}\\=\frac{1}{\sqrt[15]{ x^{28} }}\\=\frac{1}{x.\sqrt[15]{ x^{13} }}=\frac{1}{x.\sqrt[15]{ x^{13} }} \color{purple}{\frac{\sqrt[15]{ x^{2} }}{\sqrt[15]{ x^{2} }}} \\=\frac{\sqrt[15]{ x^{2} }}{x^{2}}\\---------------\)
7. \(\dfrac{x^{\frac{5}{4}}}{x^{\frac{3}{4}}}\\= x^{ \frac{5}{4} - \frac{3}{4} }= x^{\frac{1}{2}}\\= \sqrt{ x } \\---------------\)
8. \(\dfrac{x^{\frac{1}{3}}}{x^{\frac{1}{2}}}\\= x^{ \frac{1}{3} - \frac{1}{2} }= x^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ x }}=\frac{1}{\sqrt[6]{ x }}. \color{purple}{\frac{\sqrt[6]{ x^{5} }}{\sqrt[6]{ x^{5} }}} \\=\frac{\sqrt[6]{ x^{5} }}{|x|}\\---------------\)
9. \(\dfrac{q^{\frac{5}{4}}}{q^{\frac{-3}{2}}}\\= q^{ \frac{5}{4} - (\frac{-3}{2}) }= q^{\frac{11}{4}}\\=\sqrt[4]{ q^{11} }=|q^{2}|.\sqrt[4]{ q^{3} }\\---------------\)
10. \(\dfrac{y^{\frac{3}{5}}}{y^{\frac{1}{2}}}\\= y^{ \frac{3}{5} - \frac{1}{2} }= y^{\frac{1}{10}}\\=\sqrt[10]{ y }\\---------------\)
11. \(\dfrac{a^{\frac{-1}{5}}}{a^{\frac{-5}{6}}}\\= a^{ \frac{-1}{5} - (\frac{-5}{6}) }= a^{\frac{19}{30}}\\=\sqrt[30]{ a^{19} }\\---------------\)
12. \(\dfrac{a^{\frac{1}{5}}}{a^{\frac{-3}{4}}}\\= a^{ \frac{1}{5} - (\frac{-3}{4}) }= a^{\frac{19}{20}}\\=\sqrt[20]{ a^{19} }\\---------------\)