Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{-2}{5}}}{a^{\frac{1}{2}}}\\= a^{ \frac{-2}{5} - \frac{1}{2} }= a^{\frac{-9}{10}}\\=\frac{1}{\sqrt[10]{ a^{9} }}=\frac{1}{\sqrt[10]{ a^{9} }}. \color{purple}{\frac{\sqrt[10]{ a }}{\sqrt[10]{ a }}} \\=\frac{\sqrt[10]{ a }}{|a|}\\---------------\)
2. \(\dfrac{q^{\frac{3}{4}}}{q^{\frac{-5}{6}}}\\= q^{ \frac{3}{4} - (\frac{-5}{6}) }= q^{\frac{19}{12}}\\=\sqrt[12]{ q^{19} }=|q|.\sqrt[12]{ q^{7} }\\---------------\)
3. \(\dfrac{q^{\frac{3}{5}}}{q^{-1}}\\= q^{ \frac{3}{5} - (-1) }= q^{\frac{8}{5}}\\=\sqrt[5]{ q^{8} }=q.\sqrt[5]{ q^{3} }\\---------------\)
4. \(\dfrac{q^{\frac{-4}{5}}}{q^{-2}}\\= q^{ \frac{-4}{5} - (-2) }= q^{\frac{6}{5}}\\=\sqrt[5]{ q^{6} }=q.\sqrt[5]{ q }\\---------------\)
5. \(\dfrac{y^{\frac{-3}{4}}}{y^{\frac{4}{5}}}\\= y^{ \frac{-3}{4} - \frac{4}{5} }= y^{\frac{-31}{20}}\\=\frac{1}{\sqrt[20]{ y^{31} }}\\=\frac{1}{|y|.\sqrt[20]{ y^{11} }}=\frac{1}{|y|.\sqrt[20]{ y^{11} }} \color{purple}{\frac{\sqrt[20]{ y^{9} }}{\sqrt[20]{ y^{9} }}} \\=\frac{\sqrt[20]{ y^{9} }}{|y^{2}|}\\---------------\)
6. \(\dfrac{a^{-2}}{a^{\frac{1}{3}}}\\= a^{ -2 - \frac{1}{3} }= a^{\frac{-7}{3}}\\=\frac{1}{\sqrt[3]{ a^{7} }}\\=\frac{1}{a^{2}.\sqrt[3]{ a }}=\frac{1}{a^{2}.\sqrt[3]{ a }} \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a^{3}}\\---------------\)
7. \(\dfrac{x^{\frac{5}{4}}}{x^{\frac{-1}{2}}}\\= x^{ \frac{5}{4} - (\frac{-1}{2}) }= x^{\frac{7}{4}}\\=\sqrt[4]{ x^{7} }=|x|.\sqrt[4]{ x^{3} }\\---------------\)
8. \(\dfrac{a^{\frac{1}{2}}}{a^{\frac{1}{4}}}\\= a^{ \frac{1}{2} - \frac{1}{4} }= a^{\frac{1}{4}}\\=\sqrt[4]{ a }\\---------------\)
9. \(\dfrac{q^{1}}{q^{-2}}\\= q^{ 1 - (-2) }= q^{3}\\\\---------------\)
10. \(\dfrac{y^{\frac{4}{3}}}{y^{\frac{-5}{6}}}\\= y^{ \frac{4}{3} - (\frac{-5}{6}) }= y^{\frac{13}{6}}\\=\sqrt[6]{ y^{13} }=|y^{2}|.\sqrt[6]{ y }\\---------------\)
11. \(\dfrac{q^{1}}{q^{\frac{-1}{3}}}\\= q^{ 1 - (\frac{-1}{3}) }= q^{\frac{4}{3}}\\=\sqrt[3]{ q^{4} }=q.\sqrt[3]{ q }\\---------------\)
12. \(\dfrac{x^{\frac{-3}{5}}}{x^{\frac{5}{4}}}\\= x^{ \frac{-3}{5} - \frac{5}{4} }= x^{\frac{-37}{20}}\\=\frac{1}{\sqrt[20]{ x^{37} }}\\=\frac{1}{|x|.\sqrt[20]{ x^{17} }}=\frac{1}{|x|.\sqrt[20]{ x^{17} }} \color{purple}{\frac{\sqrt[20]{ x^{3} }}{\sqrt[20]{ x^{3} }}} \\=\frac{\sqrt[20]{ x^{3} }}{|x^{2}|}\\---------------\)