SOLUTION: Please help me solve these algebra problems Simplify express your answer with positive exponent 1. (- x^-2 y^3)/(5y-^2)^2 2. (a^-2/3 b^3/4)(a^1/4 b^2/3)

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Question 251328: Please help me solve these algebra problems

Simplify express your answer with positive exponent

1. (- x^-2 y^3)/(5y-^2)^2

2. (a^-2/3 b^3/4)(a^1/4 b^2/3)
Found 2 solutions by richwmiller, stanbon:
Answer by richwmiller(17219) (Show Source):
You can put this solution on YOUR website!
(- x^-2 y^3)/(5y-^2)^2
what does 5y-^2 mean?
repost with correct problem
Is it
((a^(-2/3))*(b^(3/4)))*((a^(1/4))*( b^(2/3)))
first convert all fractions to denominator 12
((a^(-8/12))*(b^(9/12)))*((a^(3/12))*( b^(8/12)))
arrange like terms
((a^(-8/12))*((a^(3/12))*( b^(8/12)))*(b^(9/12)))
((a^(-8/12))*((a^(3/12))*( b^(8/12)))*(b^(9/12)))
( b^(17/12)))/((a^(5/12))

Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
Simplify express your answer with positive exponent
Rule: x^a/x^b = x^(a-b) = 1/x^(b-a)
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1. (- x^-2 y^3)/(5y-^2)^2
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= (-x^-2 y^3)/[25y^-4)
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= (-1/25)(x^-2/1)(y^3/y^-4)
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= (-1/25)(1/x^2)(y^7/1)
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= (-y^7/25x^2)
or
= (-1/25)(y^7/x^2)
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2. (a^-2/3 b^3/4)(a^1/4 b^2/3)
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= (a^(-2/3)/a^(1/4))(b^3/b^(2/3))
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= [1/a^(1/4 + 2/3)]
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=[1/a^(11/12)]
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= [b^(7/3)]/[a^(11/12)]
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Cheers,
Stan H.