Multiply.
(-4n)^2 (2n^2)^3=
^=to the power of
To solve the given expression (-4n)^2 (2n^2)^3, we will need to simplify it by applying the rules of exponents.
First, let's deal with the expression (-4n)^2. To square a binomial, we square both the coefficient and the variable term individually:
(-4n)^2 = (-4)^2 * n^2 = 16n^2
Next, we simplify the expression (2n^2)^3. To raise a binomial to a power, we distribute the exponent to each term within the binomial:
(2n^2)^3 = (2^3 * n^2^3) = 8n^6
Now that we have simplified both parts, we can multiply them together:
16n^2 * 8n^6
To multiply variables with the same base, we add the exponents:
16 * 8 = 128
n^2 * n^6 = n^(2+6) = n^8
Combining the results, we get:
128n^8
Therefore, the simplified expression (-4n)^2 (2n^2)^3 is equal to 128n^8.