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The order of operation dictates that we deal with powers before multiplication/division and also deal with multiplication/division before addition/subtraction , that is

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n

$\\var{d}+\\var{a}\\times\\var{b}^\\var{c}$	$=$	$\\var{d}+\\var{a}\\times\\var{b^c}$
	$=$	$\\var{d}+\\var{a*b^c}$
	$=$	$\\var{ans1}$

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$\\var{d}+\\var{a}\\times\\var{b}^\\var{c}=$ [[0]]

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Note: $\\var{h}(\\var{f}-\\var{g})$ means $\\var{h}\\times(\\var{f-g})$.

The order of operation dictates that we deal with brackets (grouping symbols) before multiplication, that is

\n\n\n\n\n\n\n\n\n\n\n\n\n\n

$\\var{h}(\\var{f}-\\var{g})$	$=$	$\\var{h}(\\var{f-g})$
	$=$	$\\var{ans2}$

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$\\var{h}(\\var{f}-\\var{g})=$ [[0]]

Note: A fraction $\\frac{a}{b}$ is the same as $(a)\\div (b)$, so we have to evaluate the numerator and denominator before doing the division. We can evaluate the numerator at the same time as we evaluate the denominator.

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n

$\\displaystyle{\\var{a}+\\frac{\\var{sub}^2-(\\var{base}-\\var{sub})^2}{-\\var{base}+2\\times\\var{sub}}}$	$=$	$\\displaystyle{\\var{a}+\\frac{\\var{sub}^2-(\\var{diff})^2}{-\\var{base}+2\\times\\var{sub}}}$	(work on the innermost bracketed expression first)
	$=$	$\\displaystyle{\\var{a}+\\frac{\\var{subs}-\\var{diffs}}{-\\var{base}+2\\times\\var{sub}}}$	(doing the powers on the numerator, and multiplication on the denominator)
	$=$	$\\displaystyle{\\var{a}+\\frac{\\var{num}}{-\\var{base}+\\var{tsub}}}$	(doing multiplication on the denominator and addition on the numerator)
	$=$	$\\displaystyle{\\var{a}+\\frac{\\var{num}}{\\var{denom}}}$	(continue working on the denominator)
	$=$	$\\displaystyle{\\var{a}+\\var{base}}$	(do the division, or simplify the fraction)
	$=$	$\\var{ans3}$	(finally do the last addition)

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$\\displaystyle{\\var{a}+\\frac{\\var{sub}^2-(\\var{base}-\\var{sub})^2}{-\\var{base}+2\\times\\var{sub}}} =$ [[0]]

"}], "type": "question", "contributors": [{"name": "Angus Rosenburgh", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2048/"}]}]}], "contributors": [{"name": "Angus Rosenburgh", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2048/"}]}