Respuesta :
Answer:
Step-by-step explanation:
Given is an expression involving exponents of m and n.
We have to simplify and give the answer
Numerator is given as
[tex](3m^{-1} n^2)^4\\=\frac{3^4n^8}{m^4}[/tex]
Denominator =
[tex]((2m^{-2}n)^{3} \\=\frac{8n^3}{m^6}[/tex]
Now simplify first constant term then m term and n term
i) 81/8 is the first term
ii) [tex]\frac{\frac{1}{m^4} }{\frac{1}{m^6} } =m^2[/tex]
iii) [tex]\frac{n^8}{n^3} =n^5[/tex]
Combining everything we get
answer as
[tex]\frac{81m^2n^5}{8}[/tex]
The rule of the power of the power suggest that to solve the power of a power, multiply both the powers to simplify.
The equivalent expression of the given equation is,
[tex]x=\dfrac{6n^5}{m}[/tex]
What is equivalent expression?
Equivalent expression are the expression whose result is equal to the original expression, but the way of representation is different.
Given information-
The given expression in the problem is,
[tex]\dfrac{(3m^{-1}n^2)^4}{(2m^{-1}n)^3}[/tex]
Let the result is x. Thus,
[tex]x=\dfrac{(3m^{-1}n^2)^4}{(2m^{-1}n)^3}[/tex]
The rule of the power of the power suggest that to solve the power of a power, multiply both the powers to simplify.
Thus,
[tex]x=\dfrac{(3m^{-4}n^8)}{(2m^{-3}n^3)}[/tex]
The power of base inverse when taking the number from the denominator to numerator. Thus,
[tex]x={(3m^{-4}n^8)}{(2m^{3}n^{-3})}[/tex]
If the base is same, then the power is added,
[tex]x={(3m^{-4+3}\times n^8-3)}\\x={(6m^{-1}\times n^5)}\\\\x=\dfrac{6n^5}{m}[/tex]
Hence the equivalent expression of the given equation is,
[tex]x=\dfrac{6n^5}{m}[/tex]
Learn more about the equivalent expression here;
https://brainly.com/question/2972832
