Place the steps used to simplify the following problem in order.
(2x^-4 y^3)^2 (3x^6 y^2)
step 1: ?
step 2: ?
step 3: ?
A. 4x^-8 y^6 * 3x^6 y^2
B. 4x^-2 y^5 * 3x^6 y^2
C. 12x^-48 y^12
D. 12x^-12 y^10
E. 12x^-2 y^8
F. 12y^8/x^2
G. 12y^12/x^48
H. 12y^10/x^12
Step 1: Apply the exponent rule for raising a power to a power by multiplying the exponents within the parentheses.
(2x^-4 y^3)^2 becomes 2^2 x^-8 y^6
Step 2: Apply the exponent rule for multiplying two powers with the same base by adding the exponents.
2^2 x^-8 y^6 (3x^6 y^2) becomes 4x^-8 y^6 * 3x^6 y^2
Step 3: Apply the exponent rule for multiplying powers with the same base by adding the exponents.
4x^-8 y^6 * 3x^6 y^2 becomes 12x^-2 y^8
The correct order of steps is:
Step 1: 2^2 x^-8 y^6
Step 2: 4x^-8 y^6 * 3x^6 y^2
Step 3: 12x^-2 y^8
The answer is E. 12x^-2 y^8