Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{1}{5}}}{a^{\frac{1}{2}}}\\= a^{ \frac{1}{5} - \frac{1}{2} }= a^{\frac{-3}{10}}\\=\frac{1}{\sqrt[10]{ a^{3} }}=\frac{1}{\sqrt[10]{ a^{3} }}. \color{purple}{\frac{\sqrt[10]{ a^{7} }}{\sqrt[10]{ a^{7} }}} \\=\frac{\sqrt[10]{ a^{7} }}{|a|}\\---------------\)
2. \(\dfrac{q^{\frac{-3}{2}}}{q^{\frac{-3}{4}}}\\= q^{ \frac{-3}{2} - (\frac{-3}{4}) }= q^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ q^{3} }}=\frac{1}{\sqrt[4]{ q^{3} }}. \color{purple}{\frac{\sqrt[4]{ q }}{\sqrt[4]{ q }}} \\=\frac{\sqrt[4]{ q }}{|q|}\\---------------\)
3. \(\dfrac{y^{\frac{-3}{4}}}{y^{\frac{1}{3}}}\\= y^{ \frac{-3}{4} - \frac{1}{3} }= y^{\frac{-13}{12}}\\=\frac{1}{\sqrt[12]{ y^{13} }}\\=\frac{1}{|y|.\sqrt[12]{ y }}=\frac{1}{|y|.\sqrt[12]{ y }} \color{purple}{\frac{\sqrt[12]{ y^{11} }}{\sqrt[12]{ y^{11} }}} \\=\frac{\sqrt[12]{ y^{11} }}{|y^{2}|}\\---------------\)
4. \(\dfrac{q^{\frac{1}{3}}}{q^{\frac{-1}{6}}}\\= q^{ \frac{1}{3} - (\frac{-1}{6}) }= q^{\frac{1}{2}}\\= \sqrt{ q } \\---------------\)
5. \(\dfrac{y^{1}}{y^{\frac{-1}{3}}}\\= y^{ 1 - (\frac{-1}{3}) }= y^{\frac{4}{3}}\\=\sqrt[3]{ y^{4} }=y.\sqrt[3]{ y }\\---------------\)
6. \(\dfrac{a^{\frac{5}{4}}}{a^{\frac{2}{3}}}\\= a^{ \frac{5}{4} - \frac{2}{3} }= a^{\frac{7}{12}}\\=\sqrt[12]{ a^{7} }\\---------------\)
7. \(\dfrac{q^{\frac{-1}{2}}}{q^{\frac{-2}{3}}}\\= q^{ \frac{-1}{2} - (\frac{-2}{3}) }= q^{\frac{1}{6}}\\=\sqrt[6]{ q }\\---------------\)
8. \(\dfrac{a^{\frac{-5}{4}}}{a^{\frac{-1}{3}}}\\= a^{ \frac{-5}{4} - (\frac{-1}{3}) }= a^{\frac{-11}{12}}\\=\frac{1}{\sqrt[12]{ a^{11} }}=\frac{1}{\sqrt[12]{ a^{11} }}. \color{purple}{\frac{\sqrt[12]{ a }}{\sqrt[12]{ a }}} \\=\frac{\sqrt[12]{ a }}{|a|}\\---------------\)
9. \(\dfrac{y^{1}}{y^{\frac{1}{6}}}\\= y^{ 1 - \frac{1}{6} }= y^{\frac{5}{6}}\\=\sqrt[6]{ y^{5} }\\---------------\)
10. \(\dfrac{q^{\frac{-5}{4}}}{q^{\frac{1}{3}}}\\= q^{ \frac{-5}{4} - \frac{1}{3} }= q^{\frac{-19}{12}}\\=\frac{1}{\sqrt[12]{ q^{19} }}\\=\frac{1}{|q|.\sqrt[12]{ q^{7} }}=\frac{1}{|q|.\sqrt[12]{ q^{7} }} \color{purple}{\frac{\sqrt[12]{ q^{5} }}{\sqrt[12]{ q^{5} }}} \\=\frac{\sqrt[12]{ q^{5} }}{|q^{2}|}\\---------------\)
11. \(\dfrac{x^{\frac{1}{2}}}{x^{\frac{1}{2}}}\\= x^{ \frac{1}{2} - \frac{1}{2} }= x^{0}\\=1\\---------------\)
12. \(\dfrac{x^{\frac{-2}{5}}}{x^{\frac{3}{2}}}\\= x^{ \frac{-2}{5} - \frac{3}{2} }= x^{\frac{-19}{10}}\\=\frac{1}{\sqrt[10]{ x^{19} }}\\=\frac{1}{|x|.\sqrt[10]{ x^{9} }}=\frac{1}{|x|.\sqrt[10]{ x^{9} }} \color{purple}{\frac{\sqrt[10]{ x }}{\sqrt[10]{ x }}} \\=\frac{\sqrt[10]{ x }}{|x^{2}|}\\---------------\)