Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{-2}}{x^{\frac{5}{3}}}\\= x^{ -2 - \frac{5}{3} }= x^{\frac{-11}{3}}\\=\frac{1}{\sqrt[3]{ x^{11} }}\\=\frac{1}{x^{3}.\sqrt[3]{ x^{2} }}=\frac{1}{x^{3}.\sqrt[3]{ x^{2} }} \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x^{4}}\\---------------\)
2. \(\dfrac{x^{\frac{4}{3}}}{x^{\frac{-4}{3}}}\\= x^{ \frac{4}{3} - (\frac{-4}{3}) }= x^{\frac{8}{3}}\\=\sqrt[3]{ x^{8} }=x^{2}.\sqrt[3]{ x^{2} }\\---------------\)
3. \(\dfrac{q^{1}}{q^{-1}}\\= q^{ 1 - (-1) }= q^{2}\\\\---------------\)
4. \(\dfrac{a^{\frac{-1}{2}}}{a^{\frac{1}{2}}}\\= a^{ \frac{-1}{2} - \frac{1}{2} }= a^{-1}\\=\frac{1}{a}\\---------------\)
5. \(\dfrac{x^{\frac{-1}{4}}}{x^{\frac{-5}{3}}}\\= x^{ \frac{-1}{4} - (\frac{-5}{3}) }= x^{\frac{17}{12}}\\=\sqrt[12]{ x^{17} }=|x|.\sqrt[12]{ x^{5} }\\---------------\)
6. \(\dfrac{a^{\frac{-3}{5}}}{a^{1}}\\= a^{ \frac{-3}{5} - 1 }= a^{\frac{-8}{5}}\\=\frac{1}{\sqrt[5]{ a^{8} }}\\=\frac{1}{a.\sqrt[5]{ a^{3} }}=\frac{1}{a.\sqrt[5]{ a^{3} }} \color{purple}{\frac{\sqrt[5]{ a^{2} }}{\sqrt[5]{ a^{2} }}} \\=\frac{\sqrt[5]{ a^{2} }}{a^{2}}\\---------------\)
7. \(\dfrac{q^{-1}}{q^{\frac{4}{5}}}\\= q^{ -1 - \frac{4}{5} }= q^{\frac{-9}{5}}\\=\frac{1}{\sqrt[5]{ q^{9} }}\\=\frac{1}{q.\sqrt[5]{ q^{4} }}=\frac{1}{q.\sqrt[5]{ q^{4} }} \color{purple}{\frac{\sqrt[5]{ q }}{\sqrt[5]{ q }}} \\=\frac{\sqrt[5]{ q }}{q^{2}}\\---------------\)
8. \(\dfrac{q^{\frac{-1}{2}}}{q^{\frac{5}{4}}}\\= q^{ \frac{-1}{2} - \frac{5}{4} }= q^{\frac{-7}{4}}\\=\frac{1}{\sqrt[4]{ q^{7} }}\\=\frac{1}{|q|.\sqrt[4]{ q^{3} }}=\frac{1}{|q|.\sqrt[4]{ q^{3} }} \color{purple}{\frac{\sqrt[4]{ q }}{\sqrt[4]{ q }}} \\=\frac{\sqrt[4]{ q }}{|q^{2}|}\\---------------\)
9. \(\dfrac{y^{\frac{-3}{5}}}{y^{\frac{-1}{4}}}\\= y^{ \frac{-3}{5} - (\frac{-1}{4}) }= y^{\frac{-7}{20}}\\=\frac{1}{\sqrt[20]{ y^{7} }}=\frac{1}{\sqrt[20]{ y^{7} }}. \color{purple}{\frac{\sqrt[20]{ y^{13} }}{\sqrt[20]{ y^{13} }}} \\=\frac{\sqrt[20]{ y^{13} }}{|y|}\\---------------\)
10. \(\dfrac{a^{\frac{-1}{2}}}{a^{\frac{-1}{5}}}\\= a^{ \frac{-1}{2} - (\frac{-1}{5}) }= a^{\frac{-3}{10}}\\=\frac{1}{\sqrt[10]{ a^{3} }}=\frac{1}{\sqrt[10]{ a^{3} }}. \color{purple}{\frac{\sqrt[10]{ a^{7} }}{\sqrt[10]{ a^{7} }}} \\=\frac{\sqrt[10]{ a^{7} }}{|a|}\\---------------\)
11. \(\dfrac{y^{\frac{4}{5}}}{y^{\frac{-1}{3}}}\\= y^{ \frac{4}{5} - (\frac{-1}{3}) }= y^{\frac{17}{15}}\\=\sqrt[15]{ y^{17} }=y.\sqrt[15]{ y^{2} }\\---------------\)
12. \(\dfrac{a^{\frac{-5}{6}}}{a^{\frac{-1}{2}}}\\= a^{ \frac{-5}{6} - (\frac{-1}{2}) }= a^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ a }}=\frac{1}{\sqrt[3]{ a }}. \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a}\\---------------\)