Question

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

Answer 1

Answer:

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

Step-by-step 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 $0.01\cdot a^4\cdot x^2$