Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{1}}{q^{\frac{1}{2}}}\\= q^{ 1 - \frac{1}{2} }= q^{\frac{1}{2}}\\= \sqrt{ q } \\---------------\)
2. \(\dfrac{x^{\frac{-3}{5}}}{x^{\frac{-5}{3}}}\\= x^{ \frac{-3}{5} - (\frac{-5}{3}) }= x^{\frac{16}{15}}\\=\sqrt[15]{ x^{16} }=x.\sqrt[15]{ x }\\---------------\)
3. \(\dfrac{x^{\frac{-4}{5}}}{x^{\frac{2}{5}}}\\= x^{ \frac{-4}{5} - \frac{2}{5} }= x^{\frac{-6}{5}}\\=\frac{1}{\sqrt[5]{ x^{6} }}\\=\frac{1}{x.\sqrt[5]{ x }}=\frac{1}{x.\sqrt[5]{ x }} \color{purple}{\frac{\sqrt[5]{ x^{4} }}{\sqrt[5]{ x^{4} }}} \\=\frac{\sqrt[5]{ x^{4} }}{x^{2}}\\---------------\)
4. \(\dfrac{x^{\frac{-1}{4}}}{x^{\frac{2}{3}}}\\= x^{ \frac{-1}{4} - \frac{2}{3} }= x^{\frac{-11}{12}}\\=\frac{1}{\sqrt[12]{ x^{11} }}=\frac{1}{\sqrt[12]{ x^{11} }}. \color{purple}{\frac{\sqrt[12]{ x }}{\sqrt[12]{ x }}} \\=\frac{\sqrt[12]{ x }}{|x|}\\---------------\)
5. \(\dfrac{a^{\frac{-5}{4}}}{a^{\frac{3}{4}}}\\= a^{ \frac{-5}{4} - \frac{3}{4} }= a^{-2}\\=\frac{1}{a^{2}}\\---------------\)
6. \(\dfrac{y^{\frac{1}{2}}}{y^{\frac{-2}{5}}}\\= y^{ \frac{1}{2} - (\frac{-2}{5}) }= y^{\frac{9}{10}}\\=\sqrt[10]{ y^{9} }\\---------------\)
7. \(\dfrac{q^{\frac{5}{3}}}{q^{\frac{5}{6}}}\\= q^{ \frac{5}{3} - \frac{5}{6} }= q^{\frac{5}{6}}\\=\sqrt[6]{ q^{5} }\\---------------\)
8. \(\dfrac{y^{\frac{1}{2}}}{y^{\frac{1}{2}}}\\= y^{ \frac{1}{2} - \frac{1}{2} }= y^{0}\\=1\\---------------\)
9. \(\dfrac{a^{\frac{-1}{2}}}{a^{\frac{-3}{2}}}\\= a^{ \frac{-1}{2} - (\frac{-3}{2}) }= a^{1}\\\\---------------\)
10. \(\dfrac{q^{1}}{q^{\frac{1}{3}}}\\= q^{ 1 - \frac{1}{3} }= q^{\frac{2}{3}}\\=\sqrt[3]{ q^{2} }\\---------------\)
11. \(\dfrac{a^{1}}{a^{\frac{5}{4}}}\\= a^{ 1 - \frac{5}{4} }= a^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ a }}=\frac{1}{\sqrt[4]{ a }}. \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a|}\\---------------\)
12. \(\dfrac{x^{\frac{-3}{5}}}{x^{\frac{-1}{3}}}\\= x^{ \frac{-3}{5} - (\frac{-1}{3}) }= x^{\frac{-4}{15}}\\=\frac{1}{\sqrt[15]{ x^{4} }}=\frac{1}{\sqrt[15]{ x^{4} }}. \color{purple}{\frac{\sqrt[15]{ x^{11} }}{\sqrt[15]{ x^{11} }}} \\=\frac{\sqrt[15]{ x^{11} }}{x}\\---------------\)