simplify
(-2x^3)^2 (3x^-2)
square the first term: 4x^6
multiply it by the second term:
ans: 12x^4
(-2x^3)^2 (3x^-2)
=(-2x³)² *3/x²
=(-2)²(x³)²* 3/x²
=4x6*3 / x²
=12(x6-2)
=12x4
To simplify the expression (-2x^3)^2 * (3x^-2), we can apply the rules of exponents.
First, let's simplify the term (-2x^3)^2. To evaluate this expression, we need to square both the base (-2x^3) and the exponent 2.
(-2x^3)^2 = (-2)^2 * (x^3)^2
= 4 * x^(3*2) [When multiplying with the same base, we add the exponents]
= 4 * x^6
Now, let's simplify the term (3x^-2). Here, we have a negative exponent, so we can rewrite it as the reciprocal of x^2.
(3x^-2) = 3 * (1/x^2)
= 3/x^2
Now, let's substitute these simplified terms back into our expression:
(-2x^3)^2 * (3x^-2) = (4 * x^6) * (3/x^2)
= 12 * (x^6/x^2) [When dividing with the same base, we subtract the exponents]
= 12 * x^(6-2)
= 12 * x^4
So, the simplified expression of (-2x^3)^2 * (3x^-2) is 12x^4.