Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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