Complete the following without the use of a calculator. Use ^ to signify indices.
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\n\nIn the above example, 5 is the base and 4 is the power/exponent/index. The power signifies how many bases are multiplied together.
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", "stepsPenalty": "1", "steps": [{"type": "information", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "$\\var{base}^1$ just means there is one $\\var{base}$. So we normally don't write the power. We normally just write $\\var{base}$.
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\n
The expression $\\displaystyle\\left(\\frac{\\var{num}}{\\var{den}}\\right)^2$ is equivalent to $\\displaystyle\\frac{\\var{num}^2}{\\var{den}}$.
The square is acting on the whole fraction:
\n\\[\\left(\\frac{\\var{num}}{\\var{den}}\\right)^2=\\left(\\frac{\\var{num}}{\\var{den}}\\right)\\times\\left(\\frac{\\var{num}}{\\var{den}}\\right)=\\frac{\\var{num}^2}{\\var{den}^2}\\]
\nIn general $\\left(\\frac{a}{b}\\right)^n=\\frac{a^n}{b^n}$
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The expression $\\displaystyle\\left(\\var{num}\\times\\var{den}\\right)^2$ is equivalent to $\\displaystyle\\var{num}^2\\var{den}^2$.
The square is acting on the whole bracket:
\n\\[\\left(\\var{num}\\times\\var{den}\\right)^2=\\left(\\var{num}\\times\\var{den}\\right)\\times\\left(\\var{num}\\times\\var{den}\\right)=\\var{num}^2\\times\\var{den}^2\\]
\nIn general $\\left(ab\\right)^n=a^n b^n$
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