Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{5}{2}}}{a^{\frac{1}{4}}}\\= a^{ \frac{5}{2} - \frac{1}{4} }= a^{\frac{9}{4}}\\=\sqrt[4]{ a^{9} }=|a^{2}|.\sqrt[4]{ a }\\---------------\)
2. \(\dfrac{y^{1}}{y^{\frac{5}{4}}}\\= y^{ 1 - \frac{5}{4} }= y^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ y }}=\frac{1}{\sqrt[4]{ y }}. \color{purple}{\frac{\sqrt[4]{ y^{3} }}{\sqrt[4]{ y^{3} }}} \\=\frac{\sqrt[4]{ y^{3} }}{|y|}\\---------------\)
3. \(\dfrac{a^{\frac{1}{2}}}{a^{\frac{-3}{2}}}\\= a^{ \frac{1}{2} - (\frac{-3}{2}) }= a^{2}\\\\---------------\)
4. \(\dfrac{y^{\frac{-5}{4}}}{y^{\frac{2}{3}}}\\= y^{ \frac{-5}{4} - \frac{2}{3} }= y^{\frac{-23}{12}}\\=\frac{1}{\sqrt[12]{ y^{23} }}\\=\frac{1}{|y|.\sqrt[12]{ y^{11} }}=\frac{1}{|y|.\sqrt[12]{ y^{11} }} \color{purple}{\frac{\sqrt[12]{ y }}{\sqrt[12]{ y }}} \\=\frac{\sqrt[12]{ y }}{|y^{2}|}\\---------------\)
5. \(\dfrac{q^{\frac{5}{6}}}{q^{\frac{-1}{3}}}\\= q^{ \frac{5}{6} - (\frac{-1}{3}) }= q^{\frac{7}{6}}\\=\sqrt[6]{ q^{7} }=|q|.\sqrt[6]{ q }\\---------------\)
6. \(\dfrac{q^{\frac{-3}{2}}}{q^{\frac{-1}{5}}}\\= q^{ \frac{-3}{2} - (\frac{-1}{5}) }= q^{\frac{-13}{10}}\\=\frac{1}{\sqrt[10]{ q^{13} }}\\=\frac{1}{|q|.\sqrt[10]{ q^{3} }}=\frac{1}{|q|.\sqrt[10]{ q^{3} }} \color{purple}{\frac{\sqrt[10]{ q^{7} }}{\sqrt[10]{ q^{7} }}} \\=\frac{\sqrt[10]{ q^{7} }}{|q^{2}|}\\---------------\)
7. \(\dfrac{a^{2}}{a^{\frac{4}{3}}}\\= a^{ 2 - \frac{4}{3} }= a^{\frac{2}{3}}\\=\sqrt[3]{ a^{2} }\\---------------\)
8. \(\dfrac{a^{\frac{-2}{3}}}{a^{\frac{2}{3}}}\\= a^{ \frac{-2}{3} - \frac{2}{3} }= a^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ a^{4} }}\\=\frac{1}{a.\sqrt[3]{ a }}=\frac{1}{a.\sqrt[3]{ a }} \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a^{2}}\\---------------\)
9. \(\dfrac{y^{\frac{1}{3}}}{y^{\frac{-2}{3}}}\\= y^{ \frac{1}{3} - (\frac{-2}{3}) }= y^{1}\\\\---------------\)
10. \(\dfrac{q^{\frac{1}{2}}}{q^{\frac{-5}{4}}}\\= q^{ \frac{1}{2} - (\frac{-5}{4}) }= q^{\frac{7}{4}}\\=\sqrt[4]{ q^{7} }=|q|.\sqrt[4]{ q^{3} }\\---------------\)
11. \(\dfrac{q^{\frac{2}{3}}}{q^{1}}\\= q^{ \frac{2}{3} - 1 }= q^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ q }}=\frac{1}{\sqrt[3]{ q }}. \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q}\\---------------\)
12. \(\dfrac{y^{\frac{-5}{3}}}{y^{\frac{3}{5}}}\\= y^{ \frac{-5}{3} - \frac{3}{5} }= y^{\frac{-34}{15}}\\=\frac{1}{\sqrt[15]{ y^{34} }}\\=\frac{1}{y^{2}.\sqrt[15]{ y^{4} }}=\frac{1}{y^{2}.\sqrt[15]{ y^{4} }} \color{purple}{\frac{\sqrt[15]{ y^{11} }}{\sqrt[15]{ y^{11} }}} \\=\frac{\sqrt[15]{ y^{11} }}{y^{3}}\\---------------\)