Which of the following expressions is equivalent to (-2x^5 y^2)^4
A. -16x^20 y^8
B. -8x^10 y^8
C. -8x^9 y^6
D. 16x^9 y^6
E. 16x^20 y^8
Correction on answer choice B -8x^20 y^8*
To solve this problem, we need to understand the concept of raising a power to another power. When we have an expression raised to an exponent, and that whole expression is raised to another exponent, we can simplify it by multiplying the exponents.
In this case, we have (-2x^5 y^2)^4. To simplify this expression, we need to raise each term inside the parentheses to the power of 4.
For -2, the exponent of 4 will make it positive since any negative number raised to an even power becomes positive.
For x^5, we multiply the exponents 5 and 4 to get x^20.
For y^2, we multiply the exponents 2 and 4 to get y^8.
Putting it all together, we have (-2x^5 y^2)^4 = (-2)^4 (x^5)^4 (y^2)^4 = 16x^20 y^8.
Therefore, the correct answer is A. -16x^20 y^8.