(4j^2)^2

j^2=-1

so (-4)^2=16

(4j^2)^2

(4j^2)(4j^2) = 16j^4

To simplify the expression (4j^2)^2, you need to apply the exponent to both the base and the exponent within the parentheses.

First, let's simplify the expression within the parentheses: 4j^2.

To square a binomial, you multiply it by itself. In this case, you have a monomial (4) multiplied by a binomial (j^2).

To square 4j^2, you square both the coefficient (4) and the variable (j^2).

The coefficient of 4 squared is 4 * 4 = 16.
The variable j^2 squared is j^(2*2) = j^4.

So, (4j^2) squared simplifies to 16j^4.

Now, we can rewrite the original expression using this simplified form:

(4j^2)^2 = (16j^4) squared

To square (16j^4), you need to multiply it by itself:

(16j^4)^2 = (16j^4) * (16j^4)

To multiply monomials, you multiply the coefficients and add the exponents of the same variables.

For the coefficients, 16 * 16 = 256.

For the variables, j^4 * j^4 = j^(4+4) = j^8.

Combining these results, you get:

(16j^4) * (16j^4) = 256j^8.

So, (4j^2)^2 simplifies to 256j^8.