Werk uit m.b.v. de rekenregels
- \(\left(y^{\frac{5}{4}}\right)^{-1}\)
- \(\left(a^{\frac{-2}{5}}\right)^{-1}\)
- \(\left(a^{\frac{-1}{5}}\right)^{\frac{-5}{2}}\)
- \(\left(a^{\frac{5}{3}}\right)^{\frac{4}{3}}\)
- \(\left(q^{1}\right)^{\frac{-5}{2}}\)
- \(\left(a^{\frac{3}{5}}\right)^{\frac{-5}{4}}\)
- \(\left(y^{\frac{-1}{6}}\right)^{\frac{1}{2}}\)
- \(\left(q^{\frac{3}{4}}\right)^{1}\)
- \(\left(q^{1}\right)^{\frac{-1}{2}}\)
- \(\left(y^{\frac{1}{3}}\right)^{\frac{-2}{3}}\)
- \(\left(a^{\frac{-5}{4}}\right)^{\frac{1}{2}}\)
- \(\left(q^{1}\right)^{\frac{-5}{3}}\)
Werk uit m.b.v. de rekenregels
Verbetersleutel
- \(\left(y^{\frac{5}{4}}\right)^{-1}\\= y^{ \frac{5}{4} . (-1) }= y^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ y^{5} }}\\=\frac{1}{|y|.\sqrt[4]{ y }}=\frac{1}{|y|.\sqrt[4]{ y }}
\color{purple}{\frac{\sqrt[4]{ y^{3} }}{\sqrt[4]{ y^{3} }}} \\=\frac{\sqrt[4]{ y^{3} }}{|y^{2}|}\\---------------\)
- \(\left(a^{\frac{-2}{5}}\right)^{-1}\\= a^{ \frac{-2}{5} . (-1) }= a^{\frac{2}{5}}\\=\sqrt[5]{ a^{2} }\\---------------\)
- \(\left(a^{\frac{-1}{5}}\right)^{\frac{-5}{2}}\\= a^{ \frac{-1}{5} . (\frac{-5}{2}) }= a^{\frac{1}{2}}\\= \sqrt{ a } \\---------------\)
- \(\left(a^{\frac{5}{3}}\right)^{\frac{4}{3}}\\= a^{ \frac{5}{3} . \frac{4}{3} }= a^{\frac{20}{9}}\\=\sqrt[9]{ a^{20} }=a^{2}.\sqrt[9]{ a^{2} }\\---------------\)
- \(\left(q^{1}\right)^{\frac{-5}{2}}\\= q^{ 1 . (\frac{-5}{2}) }= q^{\frac{-5}{2}}\\=\frac{1}{ \sqrt{ q^{5} } }\\=\frac{1}{|q^{2}|. \sqrt{ q } }=\frac{1}{|q^{2}|. \sqrt{ q } }
\color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q^{3}|}\\---------------\)
- \(\left(a^{\frac{3}{5}}\right)^{\frac{-5}{4}}\\= a^{ \frac{3}{5} . (\frac{-5}{4}) }= a^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ a^{3} }}=\frac{1}{\sqrt[4]{ a^{3} }}.
\color{purple}{\frac{\sqrt[4]{ a }}{\sqrt[4]{ a }}} \\=\frac{\sqrt[4]{ a }}{|a|}\\---------------\)
- \(\left(y^{\frac{-1}{6}}\right)^{\frac{1}{2}}\\= y^{ \frac{-1}{6} . \frac{1}{2} }= y^{\frac{-1}{12}}\\=\frac{1}{\sqrt[12]{ y }}=\frac{1}{\sqrt[12]{ y }}.
\color{purple}{\frac{\sqrt[12]{ y^{11} }}{\sqrt[12]{ y^{11} }}} \\=\frac{\sqrt[12]{ y^{11} }}{|y|}\\---------------\)
- \(\left(q^{\frac{3}{4}}\right)^{1}\\= q^{ \frac{3}{4} . 1 }= q^{\frac{3}{4}}\\=\sqrt[4]{ q^{3} }\\---------------\)
- \(\left(q^{1}\right)^{\frac{-1}{2}}\\= q^{ 1 . (\frac{-1}{2}) }= q^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ q } }=\frac{1}{ \sqrt{ q } }.
\color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q|}\\---------------\)
- \(\left(y^{\frac{1}{3}}\right)^{\frac{-2}{3}}\\= y^{ \frac{1}{3} . (\frac{-2}{3}) }= y^{\frac{-2}{9}}\\=\frac{1}{\sqrt[9]{ y^{2} }}=\frac{1}{\sqrt[9]{ y^{2} }}.
\color{purple}{\frac{\sqrt[9]{ y^{7} }}{\sqrt[9]{ y^{7} }}} \\=\frac{\sqrt[9]{ y^{7} }}{y}\\---------------\)
- \(\left(a^{\frac{-5}{4}}\right)^{\frac{1}{2}}\\= a^{ \frac{-5}{4} . \frac{1}{2} }= a^{\frac{-5}{8}}\\=\frac{1}{\sqrt[8]{ a^{5} }}=\frac{1}{\sqrt[8]{ a^{5} }}.
\color{purple}{\frac{\sqrt[8]{ a^{3} }}{\sqrt[8]{ a^{3} }}} \\=\frac{\sqrt[8]{ a^{3} }}{|a|}\\---------------\)
- \(\left(q^{1}\right)^{\frac{-5}{3}}\\= q^{ 1 . (\frac{-5}{3}) }= q^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ q^{5} }}\\=\frac{1}{q.\sqrt[3]{ q^{2} }}=\frac{1}{q.\sqrt[3]{ q^{2} }}
\color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q^{2}}\\---------------\)