Simplification is the process to express an expression in simplest form. Both of their methods are correct but Alisha's method is short and easy.
What is simplification of an expression?
Simplification is the process to express an expression in simplest form.
Simplification doesn't modify the value of expression.
For the given case, the expression is
[tex]\dfrac{m^2n^{-3}}{m^6n^{-1}}[/tex]
If we cube it, it won't remain same as before (because generally, cube of a value is not itself, and its only true for -1 and 1)
(and we will need to undo it, by taking cube root, which makes this method unnecessarily long process)
The correct method is to apply the quotient of powers. This is done as;
[tex]\dfrac{m^2n^{-3}}{m^6n^{-1}} = m^{2-6}n^{-3-(-1)} = m^{-4}n^{-2} = \dfrac{1}{m^4n^2}[/tex]
Since, we have
[tex]a^b/a^c = a^{b+c} \\and\\a^b \times a^c = a^{b+c}[/tex]
Thus,
Both of their methods are correct but Alisha's method is short and easy.
Learn more about simplification here:
https://brainly.com/question/26437497
