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Question 390392: (2x^-2y^7)^-3(-4x^3)^0/(-2x^6y)^6
Answer by haileytucki(390)   (Show Source):
You can put this solution on YOUR website! simplified=
((2x^(-2)y^(7))^(-3)(-4x^(3))^(0))/((-2x^(6)y)^(6))
Remove the negative exponent in the numerator by rewriting 2x^(-2)y^(7) as (2y^(7))/(x^(2)). A negative exponent follows the rule: a^(-n)=(1)/(a^(n)).
(((2y^(7))/(x^(2)))^(-3)(-4x^(3))^(0))/((-2x^(6)y)^(6))
Expand the exponent (3) to the expression.
(1)/((2^(3)y^(7*3))/((x^(2))^(3)))*((-4x^(3))^(0))/((-2x^(6)y)^(6))
Expand the exponent (3) to the expression.
(1)/((2^(3)y^(7*3))/(x^(2*3)))*((-4x^(3))^(0))/((-2x^(6)y)^(6))
Multiply 7 by 3 to get 21.
(1)/((2^(3)y^(21))/(x^(2*3)))*((-4x^(3))^(0))/((-2x^(6)y)^(6))
Multiply 2 by 3 to get 6.
(1)/((2^(3)y^(21))/(x^(6)))*((-4x^(3))^(0))/((-2x^(6)y)^(6))
Cubing a number is the same as multiplying the number by itself 3 times (2*2*2). In this case, 2 cubed is 8.
(1)/((8y^(21))/(x^(6)))*((-4x^(3))^(0))/((-2x^(6)y)^(6))
To divide by (8y^(21))/(x^(6)), multiply by the reciprocal of the fraction.
(x^(6))/(8y^(21))*((-4x^(3))^(0))/((-2x^(6)y)^(6))
Anything raised to the 0th power is 1.
(x^(6))/(8y^(21))*(1)/((-2x^(6)y)^(6))
Raising an expression to the 6th power is the same as multiplying the expression by itself 6 times.
(x^(6))/(8y^(21))*(1)/((-2x^(6)y)(-2x^(6)y)(-2x^(6)y)(-2x^(6)y)(-2x^(6)y)(-2x^(6)y))
Multiply -2x^(6)y by -2x^(6)y to get 4x^(12)y^(2).
(x^(6))/(8y^(21))*(1)/((4x^(12)y^(2))(-2x^(6)y)(-2x^(6)y)(-2x^(6)y)(-2x^(6)y))
Multiply 4x^(12)y^(2) by -2x^(6)y to get -8x^(18)y^(3).
(x^(6))/(8y^(21))*(1)/((-8x^(18)y^(3))(-2x^(6)y)(-2x^(6)y)(-2x^(6)y))
Multiply -8x^(18)y^(3) by -2x^(6)y to get 16x^(24)y^(4).
(x^(6))/(8y^(21))*(1)/((16x^(24)y^(4))(-2x^(6)y)(-2x^(6)y))
Multiply 16x^(24)y^(4) by -2x^(6)y to get -32x^(30)y^(5).
(x^(6))/(8y^(21))*(1)/((-32x^(30)y^(5))(-2x^(6)y))
Multiply -32x^(30)y^(5) by -2x^(6)y to get 64x^(36)y^(6).
(x^(6))/(8y^(21))*(1)/(64x^(36)y^(6))
Multiply (x^(6))/(8y^(21)) by (1)/(64x^(36)y^(6)) to get (x^(6))/(512x^(36)y^(27)).
(x^(6))/(512x^(36)y^(27))
Reduce the expression (x^(6))/(512x^(36)y^(27)) by removing a factor of x^(6) from the numerator and denominator.
(1)/(512x^(30)y^(27))
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