Question
Which expression is equivalent to [tex]\frac{4mn}{m^{-2}n^6}[/tex]. Assuming [tex]m \neq 0; n\neq 0[/tex]
Answer:
[tex]\frac{4m^3}{n^5}[/tex]
Step-by-step explanation:
Given
[tex]\frac{4mn}{m^{-2}n^6}[/tex]
Required:
Simplify
To simplify this, we start by splitting each individual function
[tex]\frac{4mn}{m^{-2}n^6} = \frac{4m}{m^{-2}} * \frac{n}{n^6}[/tex]
From laws of indices
[tex]\frac{a^x}{a^y} = a^{x-y}[/tex]
SO, the above expression can also be expressed the same way
[tex]\frac{4m}{m^{-2}} * \frac{n}{n^6} = 4m^{1-(-2)} * n^{1-6}[/tex]
[tex]\frac{4m}{m^{-2}} * \frac{n}{n^6} = 4m^{1+2)} * n^{1-6}[/tex]
[tex]\frac{4m}{m^{-2}} * \frac{n}{n^6} = 4m^{3} * n^{-5}[/tex]
From laws of indices,
[tex]a^{-x} = \frac{1}{a^x}[/tex]
So,
[tex]\frac{4m}{m^{-2}} * \frac{n}{n^6} = 4m^{3} * \frac{1}{n^5}[/tex]
[tex]\frac{4m}{m^{-2}} * \frac{n}{n^6} = \frac{4m^3}{n^5}[/tex]
Hence, [tex]\frac{4mn}{m^{-2}n^6}[/tex] is equivalent to [tex]\frac{4m^3}{n^5}[/tex]
