Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{-5}{4}}}{y^{\frac{-2}{3}}}\\= y^{ \frac{-5}{4} - (\frac{-2}{3}) }= y^{\frac{-7}{12}}\\=\frac{1}{\sqrt[12]{ y^{7} }}=\frac{1}{\sqrt[12]{ y^{7} }}. \color{purple}{\frac{\sqrt[12]{ y^{5} }}{\sqrt[12]{ y^{5} }}} \\=\frac{\sqrt[12]{ y^{5} }}{|y|}\\---------------\)
2. \(\dfrac{y^{\frac{3}{5}}}{y^{\frac{-1}{3}}}\\= y^{ \frac{3}{5} - (\frac{-1}{3}) }= y^{\frac{14}{15}}\\=\sqrt[15]{ y^{14} }\\---------------\)
3. \(\dfrac{y^{\frac{2}{3}}}{y^{\frac{2}{5}}}\\= y^{ \frac{2}{3} - \frac{2}{5} }= y^{\frac{4}{15}}\\=\sqrt[15]{ y^{4} }\\---------------\)
4. \(\dfrac{q^{\frac{-1}{3}}}{q^{1}}\\= q^{ \frac{-1}{3} - 1 }= q^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ q^{4} }}\\=\frac{1}{q.\sqrt[3]{ q }}=\frac{1}{q.\sqrt[3]{ q }} \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q^{2}}\\---------------\)
5. \(\dfrac{a^{\frac{2}{5}}}{a^{\frac{-2}{3}}}\\= a^{ \frac{2}{5} - (\frac{-2}{3}) }= a^{\frac{16}{15}}\\=\sqrt[15]{ a^{16} }=a.\sqrt[15]{ a }\\---------------\)
6. \(\dfrac{q^{\frac{1}{5}}}{q^{\frac{3}{5}}}\\= q^{ \frac{1}{5} - \frac{3}{5} }= q^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ q^{2} }}=\frac{1}{\sqrt[5]{ q^{2} }}. \color{purple}{\frac{\sqrt[5]{ q^{3} }}{\sqrt[5]{ q^{3} }}} \\=\frac{\sqrt[5]{ q^{3} }}{q}\\---------------\)
7. \(\dfrac{x^{\frac{1}{2}}}{x^{\frac{-1}{6}}}\\= x^{ \frac{1}{2} - (\frac{-1}{6}) }= x^{\frac{2}{3}}\\=\sqrt[3]{ x^{2} }\\---------------\)
8. \(\dfrac{q^{1}}{q^{1}}\\= q^{ 1 - 1 }= q^{0}\\=1\\---------------\)
9. \(\dfrac{q^{\frac{1}{2}}}{q^{\frac{-5}{4}}}\\= q^{ \frac{1}{2} - (\frac{-5}{4}) }= q^{\frac{7}{4}}\\=\sqrt[4]{ q^{7} }=|q|.\sqrt[4]{ q^{3} }\\---------------\)
10. \(\dfrac{q^{2}}{q^{\frac{-2}{5}}}\\= q^{ 2 - (\frac{-2}{5}) }= q^{\frac{12}{5}}\\=\sqrt[5]{ q^{12} }=q^{2}.\sqrt[5]{ q^{2} }\\---------------\)
11. \(\dfrac{q^{\frac{-3}{5}}}{q^{1}}\\= q^{ \frac{-3}{5} - 1 }= q^{\frac{-8}{5}}\\=\frac{1}{\sqrt[5]{ q^{8} }}\\=\frac{1}{q.\sqrt[5]{ q^{3} }}=\frac{1}{q.\sqrt[5]{ q^{3} }} \color{purple}{\frac{\sqrt[5]{ q^{2} }}{\sqrt[5]{ q^{2} }}} \\=\frac{\sqrt[5]{ q^{2} }}{q^{2}}\\---------------\)
12. \(\dfrac{x^{\frac{-2}{3}}}{x^{\frac{1}{6}}}\\= x^{ \frac{-2}{3} - \frac{1}{6} }= x^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ x^{5} }}=\frac{1}{\sqrt[6]{ x^{5} }}. \color{purple}{\frac{\sqrt[6]{ x }}{\sqrt[6]{ x }}} \\=\frac{\sqrt[6]{ x }}{|x|}\\---------------\)