Answer: Choice A, x^12y^3
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Explanation:
Think of x^4y as x^4y^1. When we raise this to the third power, we multiply the outer exponent 3 by each inner exponent
x^4 turns into x^12
y^1 turns into y^3
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This is one way to show your work
(x^4y)^3
(x^4y^1)^3
x^(4*3)*y^(1*3) ... multiplying outer exponent by each inner exponent
x^12y^3
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A more lengthy way to get the answer is to write x^4y out three times multiplying by itself that many times. The outer exponent 3 tells us we will have three copies of x^4y multiplied with itself.
(x^4y)^3 = (x^4y)*(x^4y)*(x^4y)
(x^4y)^3 = (x^4*x^4*x^4)*(y*y*y)
(x^4y)^3 = ( x^(4+4+4) ) * ( y^(1+1+1) )
(x^4y)^3 = x^12y^3
