Werk uit m.b.v. de rekenregels
- \(\dfrac{a^{\frac{-1}{4}}}{a^{-2}}\)
- \(\dfrac{a^{1}}{a^{\frac{-1}{2}}}\)
- \(\dfrac{y^{1}}{y^{\frac{-1}{3}}}\)
- \(\dfrac{q^{\frac{1}{4}}}{q^{\frac{1}{2}}}\)
- \(\dfrac{y^{\frac{-1}{2}}}{y^{1}}\)
- \(\dfrac{a^{\frac{5}{2}}}{a^{\frac{3}{5}}}\)
- \(\dfrac{y^{\frac{2}{3}}}{y^{\frac{-5}{4}}}\)
- \(\dfrac{y^{1}}{y^{-1}}\)
- \(\dfrac{q^{-1}}{q^{\frac{4}{5}}}\)
- \(\dfrac{x^{\frac{-3}{2}}}{x^{\frac{-3}{5}}}\)
- \(\dfrac{y^{1}}{y^{\frac{-3}{5}}}\)
- \(\dfrac{y^{-1}}{y^{\frac{1}{2}}}\)
Werk uit m.b.v. de rekenregels
Verbetersleutel
- \(\dfrac{a^{\frac{-1}{4}}}{a^{-2}}\\= a^{ \frac{-1}{4} - (-2) }= a^{\frac{7}{4}}\\=\sqrt[4]{ a^{7} }=|a|.\sqrt[4]{ a^{3} }\\---------------\)
- \(\dfrac{a^{1}}{a^{\frac{-1}{2}}}\\= a^{ 1 - (\frac{-1}{2}) }= a^{\frac{3}{2}}\\= \sqrt{ a^{3} } =|a|. \sqrt{ a } \\---------------\)
- \(\dfrac{y^{1}}{y^{\frac{-1}{3}}}\\= y^{ 1 - (\frac{-1}{3}) }= y^{\frac{4}{3}}\\=\sqrt[3]{ y^{4} }=y.\sqrt[3]{ y }\\---------------\)
- \(\dfrac{q^{\frac{1}{4}}}{q^{\frac{1}{2}}}\\= q^{ \frac{1}{4} - \frac{1}{2} }= q^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ q }}=\frac{1}{\sqrt[4]{ q }}.
\color{purple}{\frac{\sqrt[4]{ q^{3} }}{\sqrt[4]{ q^{3} }}} \\=\frac{\sqrt[4]{ q^{3} }}{|q|}\\---------------\)
- \(\dfrac{y^{\frac{-1}{2}}}{y^{1}}\\= y^{ \frac{-1}{2} - 1 }= y^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ y^{3} } }\\=\frac{1}{|y|. \sqrt{ y } }=\frac{1}{|y|. \sqrt{ y } }
\color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y^{2}|}\\---------------\)
- \(\dfrac{a^{\frac{5}{2}}}{a^{\frac{3}{5}}}\\= a^{ \frac{5}{2} - \frac{3}{5} }= a^{\frac{19}{10}}\\=\sqrt[10]{ a^{19} }=|a|.\sqrt[10]{ a^{9} }\\---------------\)
- \(\dfrac{y^{\frac{2}{3}}}{y^{\frac{-5}{4}}}\\= y^{ \frac{2}{3} - (\frac{-5}{4}) }= y^{\frac{23}{12}}\\=\sqrt[12]{ y^{23} }=|y|.\sqrt[12]{ y^{11} }\\---------------\)
- \(\dfrac{y^{1}}{y^{-1}}\\= y^{ 1 - (-1) }= y^{2}\\\\---------------\)
- \(\dfrac{q^{-1}}{q^{\frac{4}{5}}}\\= q^{ -1 - \frac{4}{5} }= q^{\frac{-9}{5}}\\=\frac{1}{\sqrt[5]{ q^{9} }}\\=\frac{1}{q.\sqrt[5]{ q^{4} }}=\frac{1}{q.\sqrt[5]{ q^{4} }}
\color{purple}{\frac{\sqrt[5]{ q }}{\sqrt[5]{ q }}} \\=\frac{\sqrt[5]{ q }}{q^{2}}\\---------------\)
- \(\dfrac{x^{\frac{-3}{2}}}{x^{\frac{-3}{5}}}\\= x^{ \frac{-3}{2} - (\frac{-3}{5}) }= x^{\frac{-9}{10}}\\=\frac{1}{\sqrt[10]{ x^{9} }}=\frac{1}{\sqrt[10]{ x^{9} }}.
\color{purple}{\frac{\sqrt[10]{ x }}{\sqrt[10]{ x }}} \\=\frac{\sqrt[10]{ x }}{|x|}\\---------------\)
- \(\dfrac{y^{1}}{y^{\frac{-3}{5}}}\\= y^{ 1 - (\frac{-3}{5}) }= y^{\frac{8}{5}}\\=\sqrt[5]{ y^{8} }=y.\sqrt[5]{ y^{3} }\\---------------\)
- \(\dfrac{y^{-1}}{y^{\frac{1}{2}}}\\= y^{ -1 - \frac{1}{2} }= y^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ y^{3} } }\\=\frac{1}{|y|. \sqrt{ y } }=\frac{1}{|y|. \sqrt{ y } }
\color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y^{2}|}\\---------------\)