Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{4}{5}}}{y^{1}}\\= y^{ \frac{4}{5} - 1 }= y^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ y }}=\frac{1}{\sqrt[5]{ y }}. \color{purple}{\frac{\sqrt[5]{ y^{4} }}{\sqrt[5]{ y^{4} }}} \\=\frac{\sqrt[5]{ y^{4} }}{y}\\---------------\)
2. \(\dfrac{y^{\frac{-3}{2}}}{y^{\frac{5}{3}}}\\= y^{ \frac{-3}{2} - \frac{5}{3} }= y^{\frac{-19}{6}}\\=\frac{1}{\sqrt[6]{ y^{19} }}\\=\frac{1}{|y^{3}|.\sqrt[6]{ y }}=\frac{1}{|y^{3}|.\sqrt[6]{ y }} \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y^{4}|}\\---------------\)
3. \(\dfrac{y^{\frac{5}{6}}}{y^{\frac{-3}{4}}}\\= y^{ \frac{5}{6} - (\frac{-3}{4}) }= y^{\frac{19}{12}}\\=\sqrt[12]{ y^{19} }=|y|.\sqrt[12]{ y^{7} }\\---------------\)
4. \(\dfrac{q^{\frac{-1}{4}}}{q^{\frac{5}{2}}}\\= q^{ \frac{-1}{4} - \frac{5}{2} }= q^{\frac{-11}{4}}\\=\frac{1}{\sqrt[4]{ q^{11} }}\\=\frac{1}{|q^{2}|.\sqrt[4]{ q^{3} }}=\frac{1}{|q^{2}|.\sqrt[4]{ q^{3} }} \color{purple}{\frac{\sqrt[4]{ q }}{\sqrt[4]{ q }}} \\=\frac{\sqrt[4]{ q }}{|q^{3}|}\\---------------\)
5. \(\dfrac{a^{\frac{1}{3}}}{a^{-1}}\\= a^{ \frac{1}{3} - (-1) }= a^{\frac{4}{3}}\\=\sqrt[3]{ a^{4} }=a.\sqrt[3]{ a }\\---------------\)
6. \(\dfrac{a^{\frac{-5}{2}}}{a^{\frac{4}{5}}}\\= a^{ \frac{-5}{2} - \frac{4}{5} }= a^{\frac{-33}{10}}\\=\frac{1}{\sqrt[10]{ a^{33} }}\\=\frac{1}{|a^{3}|.\sqrt[10]{ a^{3} }}=\frac{1}{|a^{3}|.\sqrt[10]{ a^{3} }} \color{purple}{\frac{\sqrt[10]{ a^{7} }}{\sqrt[10]{ a^{7} }}} \\=\frac{\sqrt[10]{ a^{7} }}{|a^{4}|}\\---------------\)
7. \(\dfrac{a^{1}}{a^{\frac{-4}{5}}}\\= a^{ 1 - (\frac{-4}{5}) }= a^{\frac{9}{5}}\\=\sqrt[5]{ a^{9} }=a.\sqrt[5]{ a^{4} }\\---------------\)
8. \(\dfrac{x^{-1}}{x^{\frac{-1}{3}}}\\= x^{ -1 - (\frac{-1}{3}) }= x^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ x^{2} }}=\frac{1}{\sqrt[3]{ x^{2} }}. \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x}\\---------------\)
9. \(\dfrac{a^{\frac{1}{3}}}{a^{\frac{-4}{5}}}\\= a^{ \frac{1}{3} - (\frac{-4}{5}) }= a^{\frac{17}{15}}\\=\sqrt[15]{ a^{17} }=a.\sqrt[15]{ a^{2} }\\---------------\)
10. \(\dfrac{a^{\frac{-1}{4}}}{a^{\frac{1}{2}}}\\= a^{ \frac{-1}{4} - \frac{1}{2} }= a^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ a^{3} }}=\frac{1}{\sqrt[4]{ a^{3} }}. \color{purple}{\frac{\sqrt[4]{ a }}{\sqrt[4]{ a }}} \\=\frac{\sqrt[4]{ a }}{|a|}\\---------------\)
11. \(\dfrac{y^{-1}}{y^{-1}}\\= y^{ -1 - (-1) }= y^{0}\\=1\\---------------\)
12. \(\dfrac{q^{\frac{3}{2}}}{q^{\frac{3}{2}}}\\= q^{ \frac{3}{2} - \frac{3}{2} }= q^{0}\\=1\\---------------\)