Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{-1}}{x^{\frac{-1}{3}}}\\= x^{ -1 - (\frac{-1}{3}) }= x^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ x^{2} }}=\frac{1}{\sqrt[3]{ x^{2} }}. \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x}\\---------------\)
2. \(\dfrac{q^{\frac{-2}{3}}}{q^{\frac{1}{2}}}\\= q^{ \frac{-2}{3} - \frac{1}{2} }= q^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ q^{7} }}\\=\frac{1}{|q|.\sqrt[6]{ q }}=\frac{1}{|q|.\sqrt[6]{ q }} \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q^{2}|}\\---------------\)
3. \(\dfrac{q^{\frac{-3}{5}}}{q^{1}}\\= q^{ \frac{-3}{5} - 1 }= q^{\frac{-8}{5}}\\=\frac{1}{\sqrt[5]{ q^{8} }}\\=\frac{1}{q.\sqrt[5]{ q^{3} }}=\frac{1}{q.\sqrt[5]{ q^{3} }} \color{purple}{\frac{\sqrt[5]{ q^{2} }}{\sqrt[5]{ q^{2} }}} \\=\frac{\sqrt[5]{ q^{2} }}{q^{2}}\\---------------\)
4. \(\dfrac{x^{2}}{x^{1}}\\= x^{ 2 - 1 }= x^{1}\\\\---------------\)
5. \(\dfrac{y^{\frac{-1}{3}}}{y^{\frac{-5}{2}}}\\= y^{ \frac{-1}{3} - (\frac{-5}{2}) }= y^{\frac{13}{6}}\\=\sqrt[6]{ y^{13} }=|y^{2}|.\sqrt[6]{ y }\\---------------\)
6. \(\dfrac{a^{\frac{-5}{4}}}{a^{\frac{1}{3}}}\\= a^{ \frac{-5}{4} - \frac{1}{3} }= a^{\frac{-19}{12}}\\=\frac{1}{\sqrt[12]{ a^{19} }}\\=\frac{1}{|a|.\sqrt[12]{ a^{7} }}=\frac{1}{|a|.\sqrt[12]{ a^{7} }} \color{purple}{\frac{\sqrt[12]{ a^{5} }}{\sqrt[12]{ a^{5} }}} \\=\frac{\sqrt[12]{ a^{5} }}{|a^{2}|}\\---------------\)
7. \(\dfrac{q^{-2}}{q^{\frac{-3}{4}}}\\= q^{ -2 - (\frac{-3}{4}) }= q^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ q^{5} }}\\=\frac{1}{|q|.\sqrt[4]{ q }}=\frac{1}{|q|.\sqrt[4]{ q }} \color{purple}{\frac{\sqrt[4]{ q^{3} }}{\sqrt[4]{ q^{3} }}} \\=\frac{\sqrt[4]{ q^{3} }}{|q^{2}|}\\---------------\)
8. \(\dfrac{y^{1}}{y^{\frac{-1}{3}}}\\= y^{ 1 - (\frac{-1}{3}) }= y^{\frac{4}{3}}\\=\sqrt[3]{ y^{4} }=y.\sqrt[3]{ y }\\---------------\)
9. \(\dfrac{y^{\frac{1}{3}}}{y^{\frac{-1}{2}}}\\= y^{ \frac{1}{3} - (\frac{-1}{2}) }= y^{\frac{5}{6}}\\=\sqrt[6]{ y^{5} }\\---------------\)
10. \(\dfrac{y^{\frac{-1}{5}}}{y^{-1}}\\= y^{ \frac{-1}{5} - (-1) }= y^{\frac{4}{5}}\\=\sqrt[5]{ y^{4} }\\---------------\)
11. \(\dfrac{a^{\frac{-3}{5}}}{a^{\frac{-4}{3}}}\\= a^{ \frac{-3}{5} - (\frac{-4}{3}) }= a^{\frac{11}{15}}\\=\sqrt[15]{ a^{11} }\\---------------\)
12. \(\dfrac{q^{\frac{-1}{3}}}{q^{\frac{-5}{3}}}\\= q^{ \frac{-1}{3} - (\frac{-5}{3}) }= q^{\frac{4}{3}}\\=\sqrt[3]{ q^{4} }=q.\sqrt[3]{ q }\\---------------\)