\( \newcommand{\br}[1]{\left( #1\right)} \newcommand{\logpar}[1]{\log\left( #1\right)} \newcommand{\cospar}[1]{\cos\left( #1\right)} \newcommand{\sinpar}[1]{\sin\left( #1\right)} \newcommand{\tanpar}[1]{\tan\left( #1\right)} \newcommand{\arcsinpar}[1]{\sin^{-1}\!\left( #1\right)} \newcommand{\arccospar}[1]{\cos^{-1}\!\left( #1\right)} \newcommand{\arctanpar}[1]{\tan^{-1}\!\left( #1\right)} \newcommand{\asin}[1]{\sin^{-1}\! #1} \newcommand{\acos}[1]{\cos^{-1}\! #1} \newcommand{\atan}[1]{\tan^{-1}\! #1} \newcommand{\asinh}[1]{\sinh^{-1}\! #1} \newcommand{\acosh}[1]{\cosh^{-1}\! #1} \newcommand{\atanh}[1]{\tanh^{-1}\! #1} \newcommand{\logten}[1]{\log_{10}\! #1} \definecolor{explaination}{RGB}{0, 166, 226} \newcommand{\ubrace}[2][u]{ { \color{explaination}{\underbrace{ {\color{black}{#2}} }_{#1}} } } \newcommand{\obrace}[2][u]{ { \color{explaination}{\overbrace{ {\color{black}{#2}} }^{#1}} } } \definecolor{highlight}{RGB}{181, 41, 118} \newcommand{\xplain}[1]{{ \textcolor{explaination} { \footnotesize{ #1 \newline}}}} \newcommand{\hilite}[1]{{ \textcolor{highlight} { { #1 }}}} \definecolor{lightergray}{gray}{.675} \newcommand{\hide}[1]{{ \textcolor{lightergray} { \footnotesize{ #1 \newline}}}} \newcommand{\mth}[1]{ { \textcolor{black} { { \small #1 } } } } \)

Übung: Brüche als Exponenten #1

twoBasesOneRoot() VALS.base_1 VALS.base_2 random() < 0.75 VALS.root EXP_NEG ? BASE_D : BASE_N EXP_NEG ? BASE_N : BASE_D round( pow( EXP_NEG ? BASE_D : BASE_N, 1 / EXP_D ) ) round( pow( EXP_NEG ? BASE_N : BASE_D, 1 / EXP_D ) )

\Large fracParens( BASE_N, BASE_D )^{fracSmall( EXP_NEG ? -1 : 1, EXP_D )}

SOL_N / SOL_D

= fracParens( BASEF_N, BASEF_D )^{fracSmall( 1, EXP_D )}

Bestimme was in die Lücke gehört:
\Big(? \Big)^{EXP_D}=frac( BASEF_N, BASEF_D )

Bestimme was in die Lücke gehört:
\Big(\pink{frac( SOL_N, SOL_D )}\Big)^{EXP_D}=frac( BASEF_N, BASEF_D )

Daher ist fracParens( BASE_N, BASE_D )^{fracSmall( EXP_NEG ? -1 : 1, EXP_D )}=fracParens( BASEF_N, BASEF_D )^{fracSmall( 1, EXP_D )}=fraction( SOL_N, SOL_D, true, true, false, false )

So fracParens( BASEF_N, BASEF_D )^{fracSmall( 1, EXP_D )}=fraction( SOL_N, SOL_D,true, true, false, false )