Werk uit m.b.v. de rekenregels
- \(\left(a^{\frac{1}{4}}\right)^{-1}\)
- \(\left(y^{-1}\right)^{\frac{1}{2}}\)
- \(\left(y^{\frac{-3}{2}}\right)^{1}\)
- \(\left(a^{1}\right)^{\frac{-1}{2}}\)
- \(\left(y^{\frac{-1}{4}}\right)^{\frac{5}{6}}\)
- \(\left(y^{-1}\right)^{\frac{3}{5}}\)
- \(\left(x^{\frac{-1}{2}}\right)^{-1}\)
- \(\left(x^{-1}\right)^{-1}\)
- \(\left(y^{\frac{1}{3}}\right)^{\frac{-1}{2}}\)
- \(\left(q^{\frac{1}{2}}\right)^{1}\)
- \(\left(q^{\frac{-3}{4}}\right)^{\frac{-4}{3}}\)
- \(\left(x^{-1}\right)^{\frac{-3}{5}}\)
Werk uit m.b.v. de rekenregels
Verbetersleutel
- \(\left(a^{\frac{1}{4}}\right)^{-1}\\= a^{ \frac{1}{4} . (-1) }= a^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ a }}=\frac{1}{\sqrt[4]{ a }}.
\color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a|}\\---------------\)
- \(\left(y^{-1}\right)^{\frac{1}{2}}\\= y^{ -1 . \frac{1}{2} }= y^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ y } }=\frac{1}{ \sqrt{ y } }.
\color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y|}\\---------------\)
- \(\left(y^{\frac{-3}{2}}\right)^{1}\\= y^{ \frac{-3}{2} . 1 }= y^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ y^{3} } }\\=\frac{1}{|y|. \sqrt{ y } }=\frac{1}{|y|. \sqrt{ y } }
\color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y^{2}|}\\---------------\)
- \(\left(a^{1}\right)^{\frac{-1}{2}}\\= a^{ 1 . (\frac{-1}{2}) }= a^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ a } }=\frac{1}{ \sqrt{ a } }.
\color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a|}\\---------------\)
- \(\left(y^{\frac{-1}{4}}\right)^{\frac{5}{6}}\\= y^{ \frac{-1}{4} . \frac{5}{6} }= y^{\frac{-5}{24}}\\=\frac{1}{\sqrt[24]{ y^{5} }}=\frac{1}{\sqrt[24]{ y^{5} }}.
\color{purple}{\frac{\sqrt[24]{ y^{19} }}{\sqrt[24]{ y^{19} }}} \\=\frac{\sqrt[24]{ y^{19} }}{|y|}\\---------------\)
- \(\left(y^{-1}\right)^{\frac{3}{5}}\\= y^{ -1 . \frac{3}{5} }= y^{\frac{-3}{5}}\\=\frac{1}{\sqrt[5]{ y^{3} }}=\frac{1}{\sqrt[5]{ y^{3} }}.
\color{purple}{\frac{\sqrt[5]{ y^{2} }}{\sqrt[5]{ y^{2} }}} \\=\frac{\sqrt[5]{ y^{2} }}{y}\\---------------\)
- \(\left(x^{\frac{-1}{2}}\right)^{-1}\\= x^{ \frac{-1}{2} . (-1) }= x^{\frac{1}{2}}\\= \sqrt{ x } \\---------------\)
- \(\left(x^{-1}\right)^{-1}\\= x^{ -1 . (-1) }= x^{1}\\\\---------------\)
- \(\left(y^{\frac{1}{3}}\right)^{\frac{-1}{2}}\\= y^{ \frac{1}{3} . (\frac{-1}{2}) }= y^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ y }}=\frac{1}{\sqrt[6]{ y }}.
\color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y|}\\---------------\)
- \(\left(q^{\frac{1}{2}}\right)^{1}\\= q^{ \frac{1}{2} . 1 }= q^{\frac{1}{2}}\\= \sqrt{ q } \\---------------\)
- \(\left(q^{\frac{-3}{4}}\right)^{\frac{-4}{3}}\\= q^{ \frac{-3}{4} . (\frac{-4}{3}) }= q^{1}\\\\---------------\)
- \(\left(x^{-1}\right)^{\frac{-3}{5}}\\= x^{ -1 . (\frac{-3}{5}) }= x^{\frac{3}{5}}\\=\sqrt[5]{ x^{3} }\\---------------\)