Question

What is the monomial if a square of a monomial is:1 9/16 a12b6

Answer 1

`1(1)/(4)a^6b^3`

Explanation:

A square of a monomial is
`1(9)/(16)a^(12)b^6` that is
`(25)/(16)a^(12)b^(6)`

Use properties of exponents:

`(a^m)^n=a^(mn)\\ \\(a^m)/(b^m)=\left((a)/(b)\right)^m\\ \\a^mb^m=(ab)^m`

Note that

`(25)/(16)=(5^2)/(4^2)=\left((5)/(4)\right)^2\\ \\a^(12)=a^(6\cdot 2)=(a^6)^2\\ \\b^6=b^(3\cdot 2)=(b^3)^2`

Then

`(25)/(16)a^(12)b^(6)=\left((5)/(4)\right)^2\cdot (a^6)^2\cdot (b^(3))^2=\left((5)/(4)a^6b^3\right)^2`

So, the monomial is

`(5)/(4)a^6b^3=1(1)/(4)a^6b^3`