Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{-1}{3}}}{q^{\frac{-4}{5}}}\\= q^{ \frac{-1}{3} - (\frac{-4}{5}) }= q^{\frac{7}{15}}\\=\sqrt[15]{ q^{7} }\\---------------\)
2. \(\dfrac{a^{\frac{1}{4}}}{a^{1}}\\= a^{ \frac{1}{4} - 1 }= a^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ a^{3} }}=\frac{1}{\sqrt[4]{ a^{3} }}. \color{purple}{\frac{\sqrt[4]{ a }}{\sqrt[4]{ a }}} \\=\frac{\sqrt[4]{ a }}{|a|}\\---------------\)
3. \(\dfrac{x^{\frac{-5}{4}}}{x^{\frac{-1}{2}}}\\= x^{ \frac{-5}{4} - (\frac{-1}{2}) }= x^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ x^{3} }}=\frac{1}{\sqrt[4]{ x^{3} }}. \color{purple}{\frac{\sqrt[4]{ x }}{\sqrt[4]{ x }}} \\=\frac{\sqrt[4]{ x }}{|x|}\\---------------\)
4. \(\dfrac{y^{\frac{-1}{4}}}{y^{1}}\\= y^{ \frac{-1}{4} - 1 }= y^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ y^{5} }}\\=\frac{1}{|y|.\sqrt[4]{ y }}=\frac{1}{|y|.\sqrt[4]{ y }} \color{purple}{\frac{\sqrt[4]{ y^{3} }}{\sqrt[4]{ y^{3} }}} \\=\frac{\sqrt[4]{ y^{3} }}{|y^{2}|}\\---------------\)
5. \(\dfrac{x^{\frac{-4}{5}}}{x^{\frac{-1}{3}}}\\= x^{ \frac{-4}{5} - (\frac{-1}{3}) }= x^{\frac{-7}{15}}\\=\frac{1}{\sqrt[15]{ x^{7} }}=\frac{1}{\sqrt[15]{ x^{7} }}. \color{purple}{\frac{\sqrt[15]{ x^{8} }}{\sqrt[15]{ x^{8} }}} \\=\frac{\sqrt[15]{ x^{8} }}{x}\\---------------\)
6. \(\dfrac{y^{\frac{-5}{3}}}{y^{\frac{-1}{2}}}\\= y^{ \frac{-5}{3} - (\frac{-1}{2}) }= y^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ y^{7} }}\\=\frac{1}{|y|.\sqrt[6]{ y }}=\frac{1}{|y|.\sqrt[6]{ y }} \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y^{2}|}\\---------------\)
7. \(\dfrac{q^{\frac{1}{3}}}{q^{\frac{1}{5}}}\\= q^{ \frac{1}{3} - \frac{1}{5} }= q^{\frac{2}{15}}\\=\sqrt[15]{ q^{2} }\\---------------\)
8. \(\dfrac{y^{\frac{-4}{5}}}{y^{-1}}\\= y^{ \frac{-4}{5} - (-1) }= y^{\frac{1}{5}}\\=\sqrt[5]{ y }\\---------------\)
9. \(\dfrac{x^{\frac{-1}{6}}}{x^{\frac{5}{4}}}\\= x^{ \frac{-1}{6} - \frac{5}{4} }= x^{\frac{-17}{12}}\\=\frac{1}{\sqrt[12]{ x^{17} }}\\=\frac{1}{|x|.\sqrt[12]{ x^{5} }}=\frac{1}{|x|.\sqrt[12]{ x^{5} }} \color{purple}{\frac{\sqrt[12]{ x^{7} }}{\sqrt[12]{ x^{7} }}} \\=\frac{\sqrt[12]{ x^{7} }}{|x^{2}|}\\---------------\)
10. \(\dfrac{q^{\frac{2}{3}}}{q^{\frac{5}{4}}}\\= q^{ \frac{2}{3} - \frac{5}{4} }= q^{\frac{-7}{12}}\\=\frac{1}{\sqrt[12]{ q^{7} }}=\frac{1}{\sqrt[12]{ q^{7} }}. \color{purple}{\frac{\sqrt[12]{ q^{5} }}{\sqrt[12]{ q^{5} }}} \\=\frac{\sqrt[12]{ q^{5} }}{|q|}\\---------------\)
11. \(\dfrac{q^{\frac{1}{3}}}{q^{\frac{-4}{3}}}\\= q^{ \frac{1}{3} - (\frac{-4}{3}) }= q^{\frac{5}{3}}\\=\sqrt[3]{ q^{5} }=q.\sqrt[3]{ q^{2} }\\---------------\)
12. \(\dfrac{a^{-1}}{a^{2}}\\= a^{ -1 - 2 }= a^{-3}\\=\frac{1}{a^{3}}\\---------------\)