Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{2}}{a^{\frac{3}{4}}}\\= a^{ 2 - \frac{3}{4} }= a^{\frac{5}{4}}\\=\sqrt[4]{ a^{5} }=|a|.\sqrt[4]{ a }\\---------------\)
2. \(\dfrac{q^{-1}}{q^{\frac{2}{3}}}\\= q^{ -1 - \frac{2}{3} }= q^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ q^{5} }}\\=\frac{1}{q.\sqrt[3]{ q^{2} }}=\frac{1}{q.\sqrt[3]{ q^{2} }} \color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q^{2}}\\---------------\)
3. \(\dfrac{a^{\frac{3}{2}}}{a^{\frac{-3}{4}}}\\= a^{ \frac{3}{2} - (\frac{-3}{4}) }= a^{\frac{9}{4}}\\=\sqrt[4]{ a^{9} }=|a^{2}|.\sqrt[4]{ a }\\---------------\)
4. \(\dfrac{a^{\frac{-1}{4}}}{a^{\frac{2}{3}}}\\= a^{ \frac{-1}{4} - \frac{2}{3} }= a^{\frac{-11}{12}}\\=\frac{1}{\sqrt[12]{ a^{11} }}=\frac{1}{\sqrt[12]{ a^{11} }}. \color{purple}{\frac{\sqrt[12]{ a }}{\sqrt[12]{ a }}} \\=\frac{\sqrt[12]{ a }}{|a|}\\---------------\)
5. \(\dfrac{a^{\frac{-5}{4}}}{a^{\frac{2}{3}}}\\= a^{ \frac{-5}{4} - \frac{2}{3} }= a^{\frac{-23}{12}}\\=\frac{1}{\sqrt[12]{ a^{23} }}\\=\frac{1}{|a|.\sqrt[12]{ a^{11} }}=\frac{1}{|a|.\sqrt[12]{ a^{11} }} \color{purple}{\frac{\sqrt[12]{ a }}{\sqrt[12]{ a }}} \\=\frac{\sqrt[12]{ a }}{|a^{2}|}\\---------------\)
6. \(\dfrac{y^{\frac{5}{4}}}{y^{\frac{-4}{5}}}\\= y^{ \frac{5}{4} - (\frac{-4}{5}) }= y^{\frac{41}{20}}\\=\sqrt[20]{ y^{41} }=|y^{2}|.\sqrt[20]{ y }\\---------------\)
7. \(\dfrac{a^{\frac{-1}{3}}}{a^{\frac{2}{5}}}\\= a^{ \frac{-1}{3} - \frac{2}{5} }= a^{\frac{-11}{15}}\\=\frac{1}{\sqrt[15]{ a^{11} }}=\frac{1}{\sqrt[15]{ a^{11} }}. \color{purple}{\frac{\sqrt[15]{ a^{4} }}{\sqrt[15]{ a^{4} }}} \\=\frac{\sqrt[15]{ a^{4} }}{a}\\---------------\)
8. \(\dfrac{x^{\frac{-2}{5}}}{x^{\frac{-1}{3}}}\\= x^{ \frac{-2}{5} - (\frac{-1}{3}) }= x^{\frac{-1}{15}}\\=\frac{1}{\sqrt[15]{ x }}=\frac{1}{\sqrt[15]{ x }}. \color{purple}{\frac{\sqrt[15]{ x^{14} }}{\sqrt[15]{ x^{14} }}} \\=\frac{\sqrt[15]{ x^{14} }}{x}\\---------------\)
9. \(\dfrac{q^{\frac{-1}{3}}}{q^{\frac{-1}{3}}}\\= q^{ \frac{-1}{3} - (\frac{-1}{3}) }= q^{0}\\=1\\---------------\)
10. \(\dfrac{q^{\frac{-1}{4}}}{q^{\frac{4}{5}}}\\= q^{ \frac{-1}{4} - \frac{4}{5} }= q^{\frac{-21}{20}}\\=\frac{1}{\sqrt[20]{ q^{21} }}\\=\frac{1}{|q|.\sqrt[20]{ q }}=\frac{1}{|q|.\sqrt[20]{ q }} \color{purple}{\frac{\sqrt[20]{ q^{19} }}{\sqrt[20]{ q^{19} }}} \\=\frac{\sqrt[20]{ q^{19} }}{|q^{2}|}\\---------------\)
11. \(\dfrac{a^{\frac{5}{3}}}{a^{\frac{-3}{4}}}\\= a^{ \frac{5}{3} - (\frac{-3}{4}) }= a^{\frac{29}{12}}\\=\sqrt[12]{ a^{29} }=|a^{2}|.\sqrt[12]{ a^{5} }\\---------------\)
12. \(\dfrac{a^{\frac{-1}{6}}}{a^{\frac{-1}{3}}}\\= a^{ \frac{-1}{6} - (\frac{-1}{3}) }= a^{\frac{1}{6}}\\=\sqrt[6]{ a }\\---------------\)