Questions on Algebra: Exponents and operations on exponents answered by real tutors!

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Question 164695: sorry I made a mistake when I typed it in:
(4^-2 x y^-3/x^-3 y)^3 times (8^-1 x^-2 y/x^4 y^-1)^-2 = answer x^24/64y^16 - I cannot figure out how to get the 64 in the answer.: sorry I made a mistake when I typed it in:
(4^-2 x y^-3/x^-3 y)^3 times (8^-1 x^-2 y/x^4 y^-1)^-2 = answer x^24/64y^16 - I cannot figure out how to get the 64 in the answer.
Answer by Fombitz(1782) About Me  (Show Source):
You can put this solution on YOUR website!
Let's take each chunk step by step.
First part:
((4^(-2)*x*y^(-3))/(x^(-3)*y))^(3)=((4^(-6)*x^(3)*y^(-9))/(x^(-9)*y^3))
((4^(-2)*x*y^(-3))/(x^(-3)*y))^(3)=(4^(-6)*x^(3-(-9))*y^(-9-3)))
((4^(-2)*x*y^(-3))/(x^(-3)*y))^(3)=(4^(-6)*x^(12)*y^(-12)))
Second part:
((8^(-1)*x^(-2)*y)/(x^(4)*y^(-1)))^(-2)= (8^(2)*x^(4)*y^(-2))/(x^(-8)*y^(2))
((8^(-1)*x^(-2)*y)/(x^(4)*y^(-1)))^(-2)= (8^(2)*x^(4-(-8))*y^(-2-2)))
((8^(-1)*x^(-2)*y)/(x^(4)*y^(-1)))^(-2)= (8^(2)*x^(12)*y^(-4)))
Now let's multiply the first part by the second part:
(4^(-6)*x^(12)*y^(-12))*(8^(2)*x^(12)*y^(-4))=4^(-6)*8^(2)*x^(12+12)*y^(-12-4)
(4^(-6)*x^(12)*y^(-12))*(8^(2)*x^(12)*y^(-4))=4^(-6)*8^(2)*x^(24)*y^(-16)
Let's look at the constant,
4^(-6)*8^(2)=4^(-6)*(2*4)^(2)
4^(-6)*8^(2)=4^(-6)*2^(2)*4^(2)
4^(-6)*8^(2)=4^(-6)*4*4^(2)
4^(-6)*8^(2)=4^((-6+1+2))
4^(-6)*8^(2)=4^((-3))
4^(-6)*8^(2)=1/64
There's the 64.
(4^(-6)*x^(12)*y^(-12))*(8^(2)*x^(12)*y^(-4))=(x^(24)*y^(-16))/64
Question 164695: sorry I made a mistake when I typed it in:
(4^-2 x y^-3/x^-3 y)^3 times (8^-1 x^-2 y/x^4 y^-1)^-2 = answer x^24/64y^16 - I cannot figure out how to get the 64 in the answer.: sorry I made a mistake when I typed it in:
(4^-2 x y^-3/x^-3 y)^3 times (8^-1 x^-2 y/x^4 y^-1)^-2 = answer x^24/64y^16 - I cannot figure out how to get the 64 in the answer.
Answer by Mathtut(1309) About Me  (Show Source):
You can put this solution on YOUR website!
when you cube the 1st term out you get (4^-6*x^3*y^-9/x^-9*y^3) the second term invert and square you get (x^8*y^-2/8^-2*x^-4*y^2) when you switch 8^-2 to the numerator you have 8^2 or 8squared and when you switch 4^-6 to the denominator you get 4^6 or 4*4*4*4*4*4 when you simplify 8^2/4^6 you get 1/64....that is where the 64 comes into play in the answer....