Question

What is the monomial if a square of a monomial is: 0.0001*a^8*x^4

Answer 1

Monomial
`0.0001\cdot a^8\cdot x^4` is a square of monomial
`0.01\cdot a^4\cdot x^2`

Explanation:

Given monomial
`0.0001\cdot a^8\cdot x^4`

Using property
`(a^m)^n=a^(m\cdot n),` note that

`0.0001=(0.01)^2\\ \\a^8=(a^4)^2\\ \\x^4=(x^2)^2`

So,

`0.0001\cdot a^8\cdot x^4=(0.01)^2\cdot (a^4)^2\cdot (x^2)^2.`

Now use property
`(a\cdot b)^n=a^n\cdot b^n` to rewrite the previous expression:

`(0.01)^2\cdot (a^4)^2\cdot (x^2)^2=(0.01\cdot a^4\cdot x^2)^2`

Hence, monomial
`0.0001\cdot a^8\cdot x^4` is a square of monomial
`0.01\cdot a^4\cdot x^2`