puissance 0

n =

Nouvel énoncé

n =

Aide

Aide

Juste

Faux

Juste

Faux

RAZ

n =

Aide

Juste

Faux

Commencer la série d'exercices

\text{Dans cette série d'exercices, vous allez devoir écrire sous la forme }a^n\text{ des expressions } \
\text{du type } a^ma^p\text{, ou }\frac{a^m}{a^p}\text{, ou } \left(a^m\right)^p\text{ ; }m\text{ et }p\text{ étant des nombres entiers relatifs. }

Mathématiques à Valin

n=

\text{Dernier exercice de cette série}

montre2 = false
p = -2 (slider from -13 to 14, step 1)
n = -2 (slider from -12 to 13, step 1)
reponsea2 = NaN
finsup = If(reponsea2 ≟ 0, "=1", "")
repondu2 = Defined(reponsea2)
justea2: reponsea2 ≟ n - p
mm2 = If(exposanta2 ≟ "", "n", If[reponsea2 ≠ 1, exposanta2, ""])
puissancesa: {"1", "a", "a×a", "a×a×a", "a×a×a×a", "a×a×a×a×a", "a×a×a×a×a×a", "a×a×a×a×a×a×a", "a×a×a×a×a×a×a×a", "a×a×a×a×a×a×a×a×a", "a×a×a×a×a×a×a×a×a×a", "a×a×a×a×a×a×a×a×a×a×a", "a×a×a×a×a×a×a×a×a×a×a×a", "a×a×a×a×a×a×a×a×a×a×a×a×a"}
pan = Element(puissancesa, n + 1)
puissancesb: {"1", "b", "b×b", "b×b×b", "b×b×b×b", "b×b×b×b×b", "b×b×b×b×b×b", "b×b×b×b×b×b×b", "b×b×b×b×b×b×b×b", "b×b×b×b×b×b×b×b×b", "b×b×b×b×b×b×b×b×b×b", "b×b×b×b×b×b×b×b×b×b×b", "b×b×b×b×b×b×b×b×b×b×b×b", "b×b×b×b×b×b×b×b×b×b×b×b×b"}
pb = Element(puissancesb, p + 1)
Puissancesam = Sequence(("\frac{1}{" * Element[puissancesa, k]) + "}", k, 2, 13)
pman = Element(Puissancesam, (-n))
pAn = If(n  <  0, pman, pan)
pap = Element(puissancesa, p + 1)
pmap = Element(Puissancesam, (-p))
pAp = If(p  <  0, pmap, pap)
deroule: "=\textcolor{red}{" + pAn + " }×\textcolor{blue}{" + pAp + " }"
montre = false
longproduit = If(montre, deroule, "")
ChampTexte1 = Textfield(exposanta)
reponsea1 = NaN
mm = If(exposanta ≟ "", "n", If[reponsea1 ≠ 1, exposanta, ""])
justea1: reponsea1 ≟ n + p
deroule2: "=\frac{\textcolor{red}{ " + (LaTeX[pAn]) + " }}{\textcolor{blue}{ " + (LaTeX[pAp]) + " }}"
n': (-n)
p': (-p)
pman' = Element(Puissancesam, n)
ChampTexte2 = Textfield(exposanta2)
longquotient = If(montre2, deroule2, "")
voirjuste1 = true
expoa1 = If(n ≠ 1, "^{" + n + "}", "")
expoa2 = If(p ≠ 1, "^{" + p + "}", "")
pmap' = Element(puissancesa, (-p) + 1)
pmap2 = Element(Puissancesam, p)
gain1 = 1
repondu1 = Defined(reponsea1)
score = 0
numexo = 1
gain2 = 1
base: (2 * numexo)
fin1 = If((n > 0) ∧ (p > 0) ∨ (¬repondu2) ∧ (¬montre2) ∨ repondu2 ∧ (¬justea2) ∧ (¬montre2), "=a^{" + mm2 + "}" + finsup, "")
texte2: "\frac{\textcolor{red}{a" + (LaTeX[expoa1]) + "}}{\textcolor{blue}{a" + (LaTeX[expoa2]) + "}}" + (LaTeX[longquotient]) + "" + (LaTeX[fin1]) + ""
fin2: "=a^{" + mm2 + "}" + finsup + ""
texte3: "\frac{\textcolor{red}{a " + (LaTeX[expoa1]) + "}}{\textcolor{blue}{a " + (LaTeX[expoa2]) + "}}=\textcolor{red}{" + (LaTeX[pAn]) + "}×\textcolor{blue}{" + (LaTeX[pmap']) + "}" + (LaTeX[fin2]) + ""
texte4: "\frac{\textcolor{red}{a" + (LaTeX[expoa1]) + " }}{\textcolor{blue}{a" + (LaTeX[expoa2]) + " }}=\textcolor{red}{" + (LaTeX[pAn]) + " }×\textcolor{blue}{" + (LaTeX[pmap']) + " }" + (LaTeX[fin2]) + ""
texte5: "\frac{\textcolor{red}{a" + (LaTeX[expoa1]) + " }}{\textcolor{blue}{a" + (LaTeX[expoa2]) + " }}=\textcolor{red}{" + (LaTeX[pAn]) + " }×\textcolor{blue}{" + (LaTeX[pmap2]) + " }" + (LaTeX[fin2]) + ""
type = 3
pAn1: "\textcolor{red}{" + pAn + "}"
pAn2: "×\textcolor{red}{" + pAn + "}"
pAn3: pAn2
pAn4: pAn2
pAn2b = If(abs(p) > 1, pAn2, "")
pAn3b = If(abs(p) > 2, pAn3, "")
pAn4b = If(abs(p) > 3, pAn4, "")
pAn1b = If(abs(p) > 0, pAn1, "")
texte11: "" + (LaTeX[pAn1b]) + "" + (LaTeX[pAn2b]) + "" + (LaTeX[pAn3b]) + "" + (LaTeX[pAn4b]) + ""
texte12: "\frac{1}{" + (LaTeX[pAn1b]) + "" + (LaTeX[pAn2b]) + "" + (LaTeX[pAn3b]) + "" + (LaTeX[pAn4b]) + "}"
montre3 = false
ppuissance = If(p > 0, "=" + texte11, "=" + texte12)
longuepuissance = If(montre3, ppuissance, "")
ChampTexte3 = Textfield(exposanta3)
reponsea3 = NaN
justea3: reponsea3 ≟ (n * p)
repondu3 = Defined(reponsea3)
mm3 = If(exposanta3 ≟ "", "n", If[reponsea3 ≠ 1, exposanta3, ""])
texte10: "Score : " + score + " sur " + numexo + ""
finsup1 = If(reponsea1 ≟ 0, "=1", "")
finsup3 = If(reponsea3 ≟ 0, "=1", "")
texte13: "\left(\textcolor{red}{a^{" + (LaTeX[n]) + "}}\right)^{" + (LaTeX[p]) + "}" + (LaTeX[longuepuissance]) + "=a^{" + (LaTeX[mm3]) + "}" + (LaTeX[finsup3]) + ""
texte1: "\textcolor{red}{a" + (LaTeX[expoa1]) + "}×\textcolor{blue}{a" + (LaTeX[expoa2]) + "}" + (LaTeX[longproduit]) + "=a^{" + (LaTeX[mm]) + "}" + (LaTeX[finsup1]) + ""
debut = false
exponplusp = If(p  <  0, "" + n + "+(" + p + ")", "" + n + (("+" * p)))
nplusp: n + p
complement1 = If(nplusp ≟ 0, "=1", If[nplusp ≟ 1, "=a", ""])
texte19: "\text{Généralisation : } \\
\text{Si } n \text{ et } m \text{ sont deux entiers relatifs , } a^{n}×a^m=a^{n+m}\\
\text{Dans ce cas particulier: } a" + (LaTeX[expoa1]) + "×a" + (LaTeX[expoa2]) + " =  a^{" + (LaTeX[exponplusp]) + "}=a^{" + (LaTeX[nplusp]) + "}" + (LaTeX[complement1]) + ""
nfoisp: (n * p)
complement3 = If((n * p) ≟ 0, "=1", If[(n * p) ≟ 1, "=a", ""])
exponfoisp = If(p > 0, "" + n + "×" + p, "" + n + "×(" + p + ")")
texte20: "\text{Généralisation : } \\
\text{Si } n \text{ et } m \text{ sont deux entiers relatifs , } \left(a^{n}\right)^m=a^{n×m}\\
\text{Dans ce cas particulier: } \left(a ^{" + (LaTeX[n]) + "}\right)^{" + (LaTeX[p]) + "}  =a^{" + (LaTeX[exponfoisp]) + "}=  a^{ " + (LaTeX[nfoisp]) + "}" + (LaTeX[complement3]) + ""
nmoinsp: n - p
exponmoinsp = If(p > 0, "" + n + "-" + p, "" + n + "-(" + p + ")")
complement2 = If(n - p ≟ 0, "=1", If[n - p ≟ 1, "=a", ""])
texte21: "\text{Généralisation : } \\
\text{Si } n \text{ et } m \text{ sont deux entiers relatifs , } \frac{a^n}{a^m}=a^{n-m}\\
\text{Dans ce cas particulier: } \frac{a ^{" + (LaTeX[n]) + " }}{a^" + (LaTeX[p]) + "}  =a^{" + (LaTeX[exponmoinsp]) + "}=a^{" + (LaTeX[nmoinsp]) + "}" + (LaTeX[complement2]) + ""
grade: score
notemax: 10