Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{-1}{5}}}{y^{\frac{1}{2}}}\\= y^{ \frac{-1}{5} - \frac{1}{2} }= y^{\frac{-7}{10}}\\=\frac{1}{\sqrt[10]{ y^{7} }}=\frac{1}{\sqrt[10]{ y^{7} }}. \color{purple}{\frac{\sqrt[10]{ y^{3} }}{\sqrt[10]{ y^{3} }}} \\=\frac{\sqrt[10]{ y^{3} }}{|y|}\\---------------\)
2. \(\dfrac{a^{\frac{-1}{4}}}{a^{-1}}\\= a^{ \frac{-1}{4} - (-1) }= a^{\frac{3}{4}}\\=\sqrt[4]{ a^{3} }\\---------------\)
3. \(\dfrac{y^{\frac{-1}{2}}}{y^{\frac{-1}{3}}}\\= y^{ \frac{-1}{2} - (\frac{-1}{3}) }= y^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ y }}=\frac{1}{\sqrt[6]{ y }}. \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y|}\\---------------\)
4. \(\dfrac{q^{\frac{5}{2}}}{q^{\frac{-3}{2}}}\\= q^{ \frac{5}{2} - (\frac{-3}{2}) }= q^{4}\\\\---------------\)
5. \(\dfrac{a^{\frac{4}{5}}}{a^{\frac{-1}{3}}}\\= a^{ \frac{4}{5} - (\frac{-1}{3}) }= a^{\frac{17}{15}}\\=\sqrt[15]{ a^{17} }=a.\sqrt[15]{ a^{2} }\\---------------\)
6. \(\dfrac{y^{\frac{-1}{3}}}{y^{\frac{-5}{2}}}\\= y^{ \frac{-1}{3} - (\frac{-5}{2}) }= y^{\frac{13}{6}}\\=\sqrt[6]{ y^{13} }=|y^{2}|.\sqrt[6]{ y }\\---------------\)
7. \(\dfrac{x^{\frac{-1}{3}}}{x^{\frac{1}{2}}}\\= x^{ \frac{-1}{3} - \frac{1}{2} }= x^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ x^{5} }}=\frac{1}{\sqrt[6]{ x^{5} }}. \color{purple}{\frac{\sqrt[6]{ x }}{\sqrt[6]{ x }}} \\=\frac{\sqrt[6]{ x }}{|x|}\\---------------\)
8. \(\dfrac{x^{\frac{-3}{4}}}{x^{1}}\\= x^{ \frac{-3}{4} - 1 }= x^{\frac{-7}{4}}\\=\frac{1}{\sqrt[4]{ x^{7} }}\\=\frac{1}{|x|.\sqrt[4]{ x^{3} }}=\frac{1}{|x|.\sqrt[4]{ x^{3} }} \color{purple}{\frac{\sqrt[4]{ x }}{\sqrt[4]{ x }}} \\=\frac{\sqrt[4]{ x }}{|x^{2}|}\\---------------\)
9. \(\dfrac{a^{-1}}{a^{\frac{2}{5}}}\\= a^{ -1 - \frac{2}{5} }= a^{\frac{-7}{5}}\\=\frac{1}{\sqrt[5]{ a^{7} }}\\=\frac{1}{a.\sqrt[5]{ a^{2} }}=\frac{1}{a.\sqrt[5]{ a^{2} }} \color{purple}{\frac{\sqrt[5]{ a^{3} }}{\sqrt[5]{ a^{3} }}} \\=\frac{\sqrt[5]{ a^{3} }}{a^{2}}\\---------------\)
10. \(\dfrac{a^{\frac{-3}{5}}}{a^{\frac{1}{3}}}\\= a^{ \frac{-3}{5} - \frac{1}{3} }= a^{\frac{-14}{15}}\\=\frac{1}{\sqrt[15]{ a^{14} }}=\frac{1}{\sqrt[15]{ a^{14} }}. \color{purple}{\frac{\sqrt[15]{ a }}{\sqrt[15]{ a }}} \\=\frac{\sqrt[15]{ a }}{a}\\---------------\)
11. \(\dfrac{y^{\frac{5}{3}}}{y^{-1}}\\= y^{ \frac{5}{3} - (-1) }= y^{\frac{8}{3}}\\=\sqrt[3]{ y^{8} }=y^{2}.\sqrt[3]{ y^{2} }\\---------------\)
12. \(\dfrac{q^{\frac{2}{3}}}{q^{1}}\\= q^{ \frac{2}{3} - 1 }= q^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ q }}=\frac{1}{\sqrt[3]{ q }}. \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q}\\---------------\)