Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{-3}{5}}}{a^{\frac{3}{4}}}\\= a^{ \frac{-3}{5} - \frac{3}{4} }= a^{\frac{-27}{20}}\\=\frac{1}{\sqrt[20]{ a^{27} }}\\=\frac{1}{|a|.\sqrt[20]{ a^{7} }}=\frac{1}{|a|.\sqrt[20]{ a^{7} }} \color{purple}{\frac{\sqrt[20]{ a^{13} }}{\sqrt[20]{ a^{13} }}} \\=\frac{\sqrt[20]{ a^{13} }}{|a^{2}|}\\---------------\)
2. \(\dfrac{q^{\frac{1}{5}}}{q^{\frac{2}{5}}}\\= q^{ \frac{1}{5} - \frac{2}{5} }= q^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ q }}=\frac{1}{\sqrt[5]{ q }}. \color{purple}{\frac{\sqrt[5]{ q^{4} }}{\sqrt[5]{ q^{4} }}} \\=\frac{\sqrt[5]{ q^{4} }}{q}\\---------------\)
3. \(\dfrac{x^{\frac{-2}{3}}}{x^{\frac{-1}{5}}}\\= x^{ \frac{-2}{3} - (\frac{-1}{5}) }= x^{\frac{-7}{15}}\\=\frac{1}{\sqrt[15]{ x^{7} }}=\frac{1}{\sqrt[15]{ x^{7} }}. \color{purple}{\frac{\sqrt[15]{ x^{8} }}{\sqrt[15]{ x^{8} }}} \\=\frac{\sqrt[15]{ x^{8} }}{x}\\---------------\)
4. \(\dfrac{y^{\frac{-1}{3}}}{y^{\frac{-3}{4}}}\\= y^{ \frac{-1}{3} - (\frac{-3}{4}) }= y^{\frac{5}{12}}\\=\sqrt[12]{ y^{5} }\\---------------\)
5. \(\dfrac{q^{\frac{4}{5}}}{q^{\frac{5}{3}}}\\= q^{ \frac{4}{5} - \frac{5}{3} }= q^{\frac{-13}{15}}\\=\frac{1}{\sqrt[15]{ q^{13} }}=\frac{1}{\sqrt[15]{ q^{13} }}. \color{purple}{\frac{\sqrt[15]{ q^{2} }}{\sqrt[15]{ q^{2} }}} \\=\frac{\sqrt[15]{ q^{2} }}{q}\\---------------\)
6. \(\dfrac{q^{\frac{-1}{2}}}{q^{\frac{-1}{2}}}\\= q^{ \frac{-1}{2} - (\frac{-1}{2}) }= q^{0}\\=1\\---------------\)
7. \(\dfrac{a^{\frac{5}{4}}}{a^{\frac{-2}{5}}}\\= a^{ \frac{5}{4} - (\frac{-2}{5}) }= a^{\frac{33}{20}}\\=\sqrt[20]{ a^{33} }=|a|.\sqrt[20]{ a^{13} }\\---------------\)
8. \(\dfrac{x^{\frac{-2}{3}}}{x^{\frac{-1}{3}}}\\= x^{ \frac{-2}{3} - (\frac{-1}{3}) }= x^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ x }}=\frac{1}{\sqrt[3]{ x }}. \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x}\\---------------\)
9. \(\dfrac{y^{-1}}{y^{\frac{-3}{2}}}\\= y^{ -1 - (\frac{-3}{2}) }= y^{\frac{1}{2}}\\= \sqrt{ y } \\---------------\)
10. \(\dfrac{y^{1}}{y^{\frac{3}{4}}}\\= y^{ 1 - \frac{3}{4} }= y^{\frac{1}{4}}\\=\sqrt[4]{ y }\\---------------\)
11. \(\dfrac{q^{\frac{1}{4}}}{q^{\frac{5}{6}}}\\= q^{ \frac{1}{4} - \frac{5}{6} }= q^{\frac{-7}{12}}\\=\frac{1}{\sqrt[12]{ q^{7} }}=\frac{1}{\sqrt[12]{ q^{7} }}. \color{purple}{\frac{\sqrt[12]{ q^{5} }}{\sqrt[12]{ q^{5} }}} \\=\frac{\sqrt[12]{ q^{5} }}{|q|}\\---------------\)
12. \(\dfrac{a^{-1}}{a^{1}}\\= a^{ -1 - 1 }= a^{-2}\\=\frac{1}{a^{2}}\\---------------\)