(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.