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NB! I denne oppgaven kan du uttrykke svaret ved potenser. For eksempel kan du skrive 3^(-2)*x^7 for å få $3^{-2}\\cdot x^7$ og x^2*y for å få $x^2\\cdot y$

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Working with powers

Learn from your mistakes and have another attempt by clicking on 'Try another question like this one' until you get full marks.

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Husk potensregnereglene

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$(a\\cdot b)^n = a^n\\cdot b^n$

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$\\displaystyle{\\left(\\frac{a}{b}\\right)^n=\\frac{a^n}{b^n}}$

\n

Se eventuelt denne videoen for hjelp:

\n

", "variableReplacements": [], "marks": 0, "type": "information"}], "stepsPenalty": 0, "prompt": "

Regn ut

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$\\displaystyle{\\left(\\frac{y}{\\var{k}}\\right)^\\var{m+1}} =$[[0]]

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Husk potensregnereglene

\n

$(a\\cdot b)^n = a^n\\cdot b^n$

\n

$\\displaystyle{\\left(\\frac{a}{b}\\right)^n=\\frac{a^n}{b^n}}$

", "variableReplacements": [], "marks": 0, "type": "information"}], "stepsPenalty": "0", "prompt": "

Regn ut

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$\\displaystyle{\\left(\\var{a}x\\right)^\\var{n}} =$[[0]]

\n

", "variableReplacements": [], "marks": 0, "type": "gapfill"}, {"showCorrectAnswer": true, "scripts": {}, "variableReplacementStrategy": "originalfirst", "gaps": [{"variableReplacementStrategy": "originalfirst", "checkingaccuracy": 0.001, "expectedvariablenames": [], "showpreview": true, "variableReplacements": [], "vsetrange": [0, 1], "checkingtype": "absdiff", "type": "jme", "showCorrectAnswer": true, "scripts": {}, "checkvariablenames": false, "vsetrangepoints": 5, "answer": "{b}^{-m+1}*{-a}^{k}*y^{-m+k+1}", "marks": 1}], "steps": [{"showCorrectAnswer": true, "scripts": {}, "variableReplacementStrategy": "originalfirst", "prompt": "

Husk potensregnereglene

\n

$a^n\\cdot a^m=a^{n+m}$

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$\\displaystyle{\\frac{a^n}{a^m}=a^{n-m}}$

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", "variableReplacements": [], "marks": 0, "type": "information"}], "stepsPenalty": 0, "prompt": "

Skriv så enkelt som mulig:

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$\\displaystyle{(\\var{b}y)^\\var{-m+1}\\cdot (-\\var{a}y)^\\var{k}} =$[[0]]

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Husk potensregnereglene

\n

$a^n\\cdot a^m=a^{n+m}$

\n

$\\displaystyle{\\frac{a^n}{a^m}=a^{n-m}}$

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$\\displaystyle{\\left(a^n\\right)^m=a^{n\\cdot m}}$

", "variableReplacements": [], "marks": 0, "type": "information"}], "stepsPenalty": 0, "prompt": "

Regn ut:

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$\\displaystyle{\\left(\\var{d}\\cdot a^2\\right)^\\var{l}} =$[[0]]

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Husk potensregnereglene

\n

$a^n\\cdot a^m=a^{n+m}$

\n

$\\displaystyle{\\frac{a^n}{a^m}=a^{n-m}}$

\n

$\\displaystyle{\\left(a^n\\right)^m=a^{n\\cdot m}}$

\n

Se eventuelt denne filmsnutten for hjelp:

\n

", "variableReplacements": [], "marks": 0, "type": "information"}], "stepsPenalty": 0, "prompt": "

Skriv så enkelt som mulig:

\n

$\\displaystyle{\\frac{\\left(y^\\var{n}z\\right)^{-\\var{m}}\\cdot \\left(y z^\\var{k}\\right)^\\var{m}}{\\left(y^{-\\var{n-1}}z\\right)^\\var{m+1}}} =$[[0]]

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