Respuesta :

[tex]\bf 100x^8~~ \begin{cases} 100=10\cdot 10\\ \qquad 10^2\\ x^8=x^{4\cdot 2}\\ \qquad (x^4)^2 \end{cases}\implies 10^2(x^4)^2\implies (10x^4)^2[/tex]

facundo3141592

We want to rewrite 100*x^8 as the square of a monomial, we will find that the monomial is:

10*x^4

A monomial is a polynomial of a single term, so we want to write 100*x^8 as the square of something like:

A*x^n

Then we have:

[tex]100*x^8 = (A*x^n)^2\\\\100*x^8 = A^2*x^{2*n}[/tex]

Then we must hae:

A^2 = 100

A = √100 = 10

And:

2*n = 8

n = 8/2 = 4

Then the monomial is:

10*x^4

If you want to learn more, you can read:

https://brainly.com/question/9183135

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