Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{-1}{6}}}{a^{2}}\\= a^{ \frac{-1}{6} - 2 }= a^{\frac{-13}{6}}\\=\frac{1}{\sqrt[6]{ a^{13} }}\\=\frac{1}{|a^{2}|.\sqrt[6]{ a }}=\frac{1}{|a^{2}|.\sqrt[6]{ a }} \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a^{3}|}\\---------------\)
2. \(\dfrac{y^{\frac{1}{2}}}{y^{\frac{-4}{3}}}\\= y^{ \frac{1}{2} - (\frac{-4}{3}) }= y^{\frac{11}{6}}\\=\sqrt[6]{ y^{11} }=|y|.\sqrt[6]{ y^{5} }\\---------------\)
3. \(\dfrac{q^{-1}}{q^{\frac{3}{5}}}\\= q^{ -1 - \frac{3}{5} }= q^{\frac{-8}{5}}\\=\frac{1}{\sqrt[5]{ q^{8} }}\\=\frac{1}{q.\sqrt[5]{ q^{3} }}=\frac{1}{q.\sqrt[5]{ q^{3} }} \color{purple}{\frac{\sqrt[5]{ q^{2} }}{\sqrt[5]{ q^{2} }}} \\=\frac{\sqrt[5]{ q^{2} }}{q^{2}}\\---------------\)
4. \(\dfrac{x^{\frac{3}{5}}}{x^{\frac{4}{5}}}\\= x^{ \frac{3}{5} - \frac{4}{5} }= x^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ x }}=\frac{1}{\sqrt[5]{ x }}. \color{purple}{\frac{\sqrt[5]{ x^{4} }}{\sqrt[5]{ x^{4} }}} \\=\frac{\sqrt[5]{ x^{4} }}{x}\\---------------\)
5. \(\dfrac{y^{\frac{-1}{3}}}{y^{1}}\\= y^{ \frac{-1}{3} - 1 }= y^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ y^{4} }}\\=\frac{1}{y.\sqrt[3]{ y }}=\frac{1}{y.\sqrt[3]{ y }} \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y^{2}}\\---------------\)
6. \(\dfrac{y^{\frac{1}{5}}}{y^{\frac{-3}{5}}}\\= y^{ \frac{1}{5} - (\frac{-3}{5}) }= y^{\frac{4}{5}}\\=\sqrt[5]{ y^{4} }\\---------------\)
7. \(\dfrac{q^{-1}}{q^{\frac{2}{3}}}\\= q^{ -1 - \frac{2}{3} }= q^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ q^{5} }}\\=\frac{1}{q.\sqrt[3]{ q^{2} }}=\frac{1}{q.\sqrt[3]{ q^{2} }} \color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q^{2}}\\---------------\)
8. \(\dfrac{a^{\frac{1}{4}}}{a^{\frac{-3}{2}}}\\= a^{ \frac{1}{4} - (\frac{-3}{2}) }= a^{\frac{7}{4}}\\=\sqrt[4]{ a^{7} }=|a|.\sqrt[4]{ a^{3} }\\---------------\)
9. \(\dfrac{x^{\frac{1}{3}}}{x^{\frac{1}{5}}}\\= x^{ \frac{1}{3} - \frac{1}{5} }= x^{\frac{2}{15}}\\=\sqrt[15]{ x^{2} }\\---------------\)
10. \(\dfrac{q^{\frac{3}{5}}}{q^{\frac{3}{2}}}\\= q^{ \frac{3}{5} - \frac{3}{2} }= q^{\frac{-9}{10}}\\=\frac{1}{\sqrt[10]{ q^{9} }}=\frac{1}{\sqrt[10]{ q^{9} }}. \color{purple}{\frac{\sqrt[10]{ q }}{\sqrt[10]{ q }}} \\=\frac{\sqrt[10]{ q }}{|q|}\\---------------\)
11. \(\dfrac{x^{1}}{x^{1}}\\= x^{ 1 - 1 }= x^{0}\\=1\\---------------\)
12. \(\dfrac{a^{\frac{3}{4}}}{a^{1}}\\= a^{ \frac{3}{4} - 1 }= a^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ a }}=\frac{1}{\sqrt[4]{ a }}. \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a|}\\---------------\)