What is the monomial if a square of a monomial is: 1/4 a2n

Step-by-step explanation:

Givens:

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:

So, here we have to find the squared root of and , applying the root to each factor:

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:

Now, we solve:

Therefore, the monomial expression is

use the power rule  

( a b ) n = a n b n

to distribute the exponent.

apply the product rule to  

3 x 2 y 3 . ( 3 x 2 ) 2 ( y 3 ) 2

apply the product rule to  

3 x 2 . 3 2 ( x 2 ) 2 ( y 3 ) 2

raise  

3

to the power of  

2 . 9 ( x 2 ) 2 ( y 3 ) 2 multiply the exponents in   ( x 2 ) 2

.

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 2 ⋅ 2 ( y 3 ) 2

multiply  

2   by   2 . 9 x 4 ( y 3 ) 2

multiply the exponents in  

( y 3 ) 2 .

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 4 y 3

⋅

2

multiply  

3   by   2 . 9 x 4 y 6

step-by-step explanation: