Answer:
[tex]Standard\ Form = {3n^2} m^{-2}[/tex]
Step-by-step explanation:
Given
[tex]\frac{2}{3m^2n} * 4.5n^3[/tex]
Required
Write in Standard Form
To start with; the two monomials have to be multiplied together;
[tex]\frac{2}{3m^2n} * 4.5n^3[/tex]
[tex]Standard\ Form = \frac{2 * 4.5n^3}{3m^2n}[/tex]
Split the numerator and the denominator
[tex]Standard\ Form = \frac{2 * 4.5 * n^3}{3 * m^2 * n}[/tex]
Multiply Like terms
[tex]Standard\ Form = \frac{9 * n^3}{3 * m^2 * n}[/tex]
Divide 9 by 3 to give 3
[tex]Standard\ Form = \frac{3 * n^3}{m^2 * n}[/tex]
Divide n³ by n to n²
[tex]Standard\ Form = \frac{3 * n^2}{m^2 }[/tex]
Split fraction
[tex]Standard\ Form = {3 * n^2} * \frac{1}{m^2 }[/tex]
From laws of indices;
[tex]\frac{1}{a^n} = a^{-n}[/tex]
[tex]Standard\ Form = {3 * n^2} * \frac{1}{m^2 }[/tex] becomes
[tex]Standard\ Form = {3 * n^2} * m^{-2}[/tex]
Multiply all together
[tex]Standard\ Form = {3n^2} m^{-2}[/tex]
