Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{1}}{q^{2}}\\= q^{ 1 - 2 }= q^{-1}\\=\frac{1}{q}\\---------------\)
2. \(\dfrac{q^{2}}{q^{-1}}\\= q^{ 2 - (-1) }= q^{3}\\\\---------------\)
3. \(\dfrac{a^{2}}{a^{1}}\\= a^{ 2 - 1 }= a^{1}\\\\---------------\)
4. \(\dfrac{x^{2}}{x^{\frac{-1}{5}}}\\= x^{ 2 - (\frac{-1}{5}) }= x^{\frac{11}{5}}\\=\sqrt[5]{ x^{11} }=x^{2}.\sqrt[5]{ x }\\---------------\)
5. \(\dfrac{y^{\frac{-1}{3}}}{y^{\frac{-3}{2}}}\\= y^{ \frac{-1}{3} - (\frac{-3}{2}) }= y^{\frac{7}{6}}\\=\sqrt[6]{ y^{7} }=|y|.\sqrt[6]{ y }\\---------------\)
6. \(\dfrac{q^{\frac{5}{2}}}{q^{\frac{5}{4}}}\\= q^{ \frac{5}{2} - \frac{5}{4} }= q^{\frac{5}{4}}\\=\sqrt[4]{ q^{5} }=|q|.\sqrt[4]{ q }\\---------------\)
7. \(\dfrac{y^{\frac{3}{5}}}{y^{\frac{-1}{3}}}\\= y^{ \frac{3}{5} - (\frac{-1}{3}) }= y^{\frac{14}{15}}\\=\sqrt[15]{ y^{14} }\\---------------\)
8. \(\dfrac{a^{\frac{-3}{4}}}{a^{\frac{-1}{2}}}\\= a^{ \frac{-3}{4} - (\frac{-1}{2}) }= a^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ a }}=\frac{1}{\sqrt[4]{ a }}. \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a|}\\---------------\)
9. \(\dfrac{y^{-1}}{y^{\frac{-4}{3}}}\\= y^{ -1 - (\frac{-4}{3}) }= y^{\frac{1}{3}}\\=\sqrt[3]{ y }\\---------------\)
10. \(\dfrac{x^{\frac{-4}{3}}}{x^{\frac{3}{5}}}\\= x^{ \frac{-4}{3} - \frac{3}{5} }= x^{\frac{-29}{15}}\\=\frac{1}{\sqrt[15]{ x^{29} }}\\=\frac{1}{x.\sqrt[15]{ x^{14} }}=\frac{1}{x.\sqrt[15]{ x^{14} }} \color{purple}{\frac{\sqrt[15]{ x }}{\sqrt[15]{ x }}} \\=\frac{\sqrt[15]{ x }}{x^{2}}\\---------------\)
11. \(\dfrac{x^{\frac{5}{4}}}{x^{\frac{-5}{2}}}\\= x^{ \frac{5}{4} - (\frac{-5}{2}) }= x^{\frac{15}{4}}\\=\sqrt[4]{ x^{15} }=|x^{3}|.\sqrt[4]{ x^{3} }\\---------------\)
12. \(\dfrac{y^{\frac{3}{5}}}{y^{\frac{-1}{4}}}\\= y^{ \frac{3}{5} - (\frac{-1}{4}) }= y^{\frac{17}{20}}\\=\sqrt[20]{ y^{17} }\\---------------\)