Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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