Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{-4}{5}}}{x^{\frac{5}{3}}}\\= x^{ \frac{-4}{5} - \frac{5}{3} }= x^{\frac{-37}{15}}\\=\frac{1}{\sqrt[15]{ x^{37} }}\\=\frac{1}{x^{2}.\sqrt[15]{ x^{7} }}=\frac{1}{x^{2}.\sqrt[15]{ x^{7} }} \color{purple}{\frac{\sqrt[15]{ x^{8} }}{\sqrt[15]{ x^{8} }}} \\=\frac{\sqrt[15]{ x^{8} }}{x^{3}}\\---------------\)
2. \(\dfrac{a^{1}}{a^{\frac{-2}{3}}}\\= a^{ 1 - (\frac{-2}{3}) }= a^{\frac{5}{3}}\\=\sqrt[3]{ a^{5} }=a.\sqrt[3]{ a^{2} }\\---------------\)
3. \(\dfrac{q^{\frac{-5}{6}}}{q^{1}}\\= q^{ \frac{-5}{6} - 1 }= q^{\frac{-11}{6}}\\=\frac{1}{\sqrt[6]{ q^{11} }}\\=\frac{1}{|q|.\sqrt[6]{ q^{5} }}=\frac{1}{|q|.\sqrt[6]{ q^{5} }} \color{purple}{\frac{\sqrt[6]{ q }}{\sqrt[6]{ q }}} \\=\frac{\sqrt[6]{ q }}{|q^{2}|}\\---------------\)
4. \(\dfrac{q^{\frac{-4}{5}}}{q^{2}}\\= q^{ \frac{-4}{5} - 2 }= q^{\frac{-14}{5}}\\=\frac{1}{\sqrt[5]{ q^{14} }}\\=\frac{1}{q^{2}.\sqrt[5]{ q^{4} }}=\frac{1}{q^{2}.\sqrt[5]{ q^{4} }} \color{purple}{\frac{\sqrt[5]{ q }}{\sqrt[5]{ q }}} \\=\frac{\sqrt[5]{ q }}{q^{3}}\\---------------\)
5. \(\dfrac{q^{\frac{5}{3}}}{q^{\frac{-2}{3}}}\\= q^{ \frac{5}{3} - (\frac{-2}{3}) }= q^{\frac{7}{3}}\\=\sqrt[3]{ q^{7} }=q^{2}.\sqrt[3]{ q }\\---------------\)
6. \(\dfrac{x^{1}}{x^{\frac{-5}{3}}}\\= x^{ 1 - (\frac{-5}{3}) }= x^{\frac{8}{3}}\\=\sqrt[3]{ x^{8} }=x^{2}.\sqrt[3]{ x^{2} }\\---------------\)
7. \(\dfrac{y^{1}}{y^{\frac{-1}{3}}}\\= y^{ 1 - (\frac{-1}{3}) }= y^{\frac{4}{3}}\\=\sqrt[3]{ y^{4} }=y.\sqrt[3]{ y }\\---------------\)
8. \(\dfrac{x^{\frac{-1}{2}}}{x^{\frac{5}{3}}}\\= x^{ \frac{-1}{2} - \frac{5}{3} }= x^{\frac{-13}{6}}\\=\frac{1}{\sqrt[6]{ x^{13} }}\\=\frac{1}{|x^{2}|.\sqrt[6]{ x }}=\frac{1}{|x^{2}|.\sqrt[6]{ x }} \color{purple}{\frac{\sqrt[6]{ x^{5} }}{\sqrt[6]{ x^{5} }}} \\=\frac{\sqrt[6]{ x^{5} }}{|x^{3}|}\\---------------\)
9. \(\dfrac{y^{\frac{-4}{3}}}{y^{\frac{4}{3}}}\\= y^{ \frac{-4}{3} - \frac{4}{3} }= y^{\frac{-8}{3}}\\=\frac{1}{\sqrt[3]{ y^{8} }}\\=\frac{1}{y^{2}.\sqrt[3]{ y^{2} }}=\frac{1}{y^{2}.\sqrt[3]{ y^{2} }} \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y^{3}}\\---------------\)
10. \(\dfrac{x^{\frac{-5}{2}}}{x^{\frac{-3}{4}}}\\= x^{ \frac{-5}{2} - (\frac{-3}{4}) }= x^{\frac{-7}{4}}\\=\frac{1}{\sqrt[4]{ x^{7} }}\\=\frac{1}{|x|.\sqrt[4]{ x^{3} }}=\frac{1}{|x|.\sqrt[4]{ x^{3} }} \color{purple}{\frac{\sqrt[4]{ x }}{\sqrt[4]{ x }}} \\=\frac{\sqrt[4]{ x }}{|x^{2}|}\\---------------\)
11. \(\dfrac{q^{\frac{1}{2}}}{q^{\frac{1}{5}}}\\= q^{ \frac{1}{2} - \frac{1}{5} }= q^{\frac{3}{10}}\\=\sqrt[10]{ q^{3} }\\---------------\)
12. \(\dfrac{a^{\frac{2}{3}}}{a^{\frac{5}{4}}}\\= a^{ \frac{2}{3} - \frac{5}{4} }= a^{\frac{-7}{12}}\\=\frac{1}{\sqrt[12]{ a^{7} }}=\frac{1}{\sqrt[12]{ a^{7} }}. \color{purple}{\frac{\sqrt[12]{ a^{5} }}{\sqrt[12]{ a^{5} }}} \\=\frac{\sqrt[12]{ a^{5} }}{|a|}\\---------------\)