This is the simplest form [tex]4\sqrt{5}x^3(6\sqrt{x} -\sqrt{2})[/tex].
Exponential notation is the form of mathematical shorthand which allows us to write complicated expressions more succinctly. An exponent is a number or letter is called the base. It indicates that the base is to raise to a certain power. X is the base and n is the power.
Simplification is to make something easier to do or understand and to make something less complicated.
Given
[tex]\rm 2\sqrt{8x^3} * (3\sqrt{10x^4} - x\sqrt{5x^2} )[/tex] is an expression.
[tex]\rm 2\sqrt{8x^3} * (3\sqrt{10x^4} - x\sqrt{5x^2} )[/tex]
On simplifying, we have
[tex]\rm 4\sqrt{2} (x)^{\frac{3}{2}} * ( 3\sqrt{10} x^2 - \sqrt{5} x^{\frac{3}{2}})\\\\24\sqrt{5} x^{\frac{7}{2}} - 4\sqrt{10}x^3\\\\4\sqrt{5}x^3(6\sqrt{x} -\sqrt{2} )\\[/tex]
This is the simplest form [tex]4\sqrt{5}x^3(6\sqrt{x} -\sqrt{2})[/tex].
More about the exponent link is given below.
https://brainly.com/question/5497425
