Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{1}{2}}}{q^{\frac{3}{2}}}\\= q^{ \frac{1}{2} - \frac{3}{2} }= q^{-1}\\=\frac{1}{q}\\---------------\)
2. \(\dfrac{x^{2}}{x^{\frac{-4}{5}}}\\= x^{ 2 - (\frac{-4}{5}) }= x^{\frac{14}{5}}\\=\sqrt[5]{ x^{14} }=x^{2}.\sqrt[5]{ x^{4} }\\---------------\)
3. \(\dfrac{x^{\frac{1}{2}}}{x^{\frac{2}{5}}}\\= x^{ \frac{1}{2} - \frac{2}{5} }= x^{\frac{1}{10}}\\=\sqrt[10]{ x }\\---------------\)
4. \(\dfrac{a^{1}}{a^{\frac{-4}{3}}}\\= a^{ 1 - (\frac{-4}{3}) }= a^{\frac{7}{3}}\\=\sqrt[3]{ a^{7} }=a^{2}.\sqrt[3]{ a }\\---------------\)
5. \(\dfrac{a^{-1}}{a^{-1}}\\= a^{ -1 - (-1) }= a^{0}\\=1\\---------------\)
6. \(\dfrac{x^{-2}}{x^{\frac{1}{3}}}\\= x^{ -2 - \frac{1}{3} }= x^{\frac{-7}{3}}\\=\frac{1}{\sqrt[3]{ x^{7} }}\\=\frac{1}{x^{2}.\sqrt[3]{ x }}=\frac{1}{x^{2}.\sqrt[3]{ x }} \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x^{3}}\\---------------\)
7. \(\dfrac{q^{\frac{-4}{5}}}{q^{1}}\\= q^{ \frac{-4}{5} - 1 }= q^{\frac{-9}{5}}\\=\frac{1}{\sqrt[5]{ q^{9} }}\\=\frac{1}{q.\sqrt[5]{ q^{4} }}=\frac{1}{q.\sqrt[5]{ q^{4} }} \color{purple}{\frac{\sqrt[5]{ q }}{\sqrt[5]{ q }}} \\=\frac{\sqrt[5]{ q }}{q^{2}}\\---------------\)
8. \(\dfrac{x^{-1}}{x^{\frac{2}{3}}}\\= x^{ -1 - \frac{2}{3} }= x^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ x^{5} }}\\=\frac{1}{x.\sqrt[3]{ x^{2} }}=\frac{1}{x.\sqrt[3]{ x^{2} }} \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x^{2}}\\---------------\)
9. \(\dfrac{y^{\frac{1}{5}}}{y^{\frac{-2}{3}}}\\= y^{ \frac{1}{5} - (\frac{-2}{3}) }= y^{\frac{13}{15}}\\=\sqrt[15]{ y^{13} }\\---------------\)
10. \(\dfrac{q^{\frac{2}{5}}}{q^{-1}}\\= q^{ \frac{2}{5} - (-1) }= q^{\frac{7}{5}}\\=\sqrt[5]{ q^{7} }=q.\sqrt[5]{ q^{2} }\\---------------\)
11. \(\dfrac{a^{\frac{1}{5}}}{a^{\frac{2}{5}}}\\= a^{ \frac{1}{5} - \frac{2}{5} }= a^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ a }}=\frac{1}{\sqrt[5]{ a }}. \color{purple}{\frac{\sqrt[5]{ a^{4} }}{\sqrt[5]{ a^{4} }}} \\=\frac{\sqrt[5]{ a^{4} }}{a}\\---------------\)
12. \(\dfrac{a^{\frac{2}{3}}}{a^{\frac{5}{4}}}\\= a^{ \frac{2}{3} - \frac{5}{4} }= a^{\frac{-7}{12}}\\=\frac{1}{\sqrt[12]{ a^{7} }}=\frac{1}{\sqrt[12]{ a^{7} }}. \color{purple}{\frac{\sqrt[12]{ a^{5} }}{\sqrt[12]{ a^{5} }}} \\=\frac{\sqrt[12]{ a^{5} }}{|a|}\\---------------\)