Respuesta :
Answer:
[tex]\frac{1}{2} a^n[/tex]
Step-by-step explanation:
Square of the monomial is [tex]\frac{1}{4}a^{2n}[/tex]
To get the monomial we take square root
Lets take square root for each term
[tex]\sqrt{\frac{1}{4}a^{2n}}[/tex]
[tex]\sqrt{\frac{1}{4}}=\fract{1}{2}[/tex] because square root of 4 is 2
[tex]\sqrt{a^{2n}}=(a^{2n})^\frac{1}{2}[/tex]
2/2 is 1 so, its a^n
Required monomial is [tex]\frac{1}{2} a^n[/tex]
Answer:
[tex]\frac{1}{2}a^n[/tex]
Step-by-step explanation:
Givens:
- Square of a monomial: [tex]\frac{1}{4} a^{2n}[/tex].
The problem is asking for the monomial, and the given is squared. What we have to do is to extract that square from expression, and that it's done applying a squared root, because that's the opposite operation of a squared power:
[tex]\sqrt{\frac{1}{4} a^{2n}}[/tex]
So, here we have to find the squared root of [tex]\frac{1}{4}[/tex] and [tex]a^{2n}[/tex], applying the root to each factor:
[tex]\sqrt{\frac{1}{4}} \sqrt{a^{2n}}[/tex]
So, we know that a root can be expressed as a fractional exponent, and also the root of a fraction is the root of each part of the fraction:
[tex]\frac{\sqrt{1}}{\sqrt{4}} (a^{2n})^{\frac{1}{2} }[/tex]
Now, we solve:
[tex]\frac{1}{2}a^{\frac{2n}{2}}= \frac{1}{2}a^n[/tex]
Therefore, the monomial expression is [tex]\frac{1}{2}a^n[/tex]
