Answer:
as written: 7x^2
perhaps intended: 7x^4
Step-by-step explanation:
As written, the Order of Operations specifies that the only denominator factor is 3, so the expression is interpreted as ...
[tex]\dfrac{21x^3}{3}x^{-1}=\dfrac{21}{3}x^{3-1}=7x^2[/tex]
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Sometimes grouping of denominator factors is intended, but parentheses are not written as they should be. If the intention is ...
21x^3/(3x^-1)
then the simplification is ...
[tex]\dfrac{21x^3}{3x^{-1}}=\dfrac{21}{3}x^{3-(-1)}=7x^4[/tex]
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The applicable rules of exponents are ...
(a^b)(a^c) = a^(b+c)
a^b/a^c = a^(b-c)
