Question

What is the answer and how do you solve


21x^3/3x^−1

Answer 1

as written: 7x^2

perhaps intended: 7x^4

Explanation:

As written, the Order of Operations specifies that the only denominator factor is 3, so the expression is interpreted as ...

`(21x^3)/(3)x^(-1)=(21)/(3)x^(3-1)=7x^2`

___

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 ...

`(21x^3)/(3x^(-1))=(21)/(3)x^(3-(-1))=7x^4`

_____

The applicable rules of exponents are ...

(a^b)(a^c) = a^(b+c)

a^b/a^c = a^(b-c)