SOLUTION: Simplify, and write without negative exponents. {{{((2p^(-7)z^3)/(3q^(-2)x^(-4)))^-1}}}

Question 1102574: Simplify, and write without negative exponents.

Found 2 solutions by ankor@dixie-net.com, greenestamps:
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!

inverting the fraction eliminates the -1 exponent

reciprocal removes the neg from the exponent

Answer by greenestamps(13198) (Show Source): You can put this solution on YOUR website!

There are dozens of paths you could follow to simplify an expression like this....

Since all of the variables occur only once each, I would simplify the expression in one step by considering each variable separately.

Specifically, I would "distribute" the -1 exponent on the expression in parentheses to each factor inside the parentheses; then if the resulting exponent is positive I would leave that factor where it is (numerator or denominator), and if the resulting exponent is negative I would move that factor to the other part of the fraction.

2 in the numerator: the exponent is 1; multiplied by -1 is -1; the 2 moves to the denominator
p^-7 in the numerator: -7 times -1 is +7; the p^7 stays in the numerator
z^3 in the numerator: 3 times -1 is -3; the z^3 moves to the denominator
3 in the denominator: the exponent is 1; multiplied by -1 is -1; the 3 moves to the numerator
q^-2 in the denominator: -2 times -1 is +2; the q^2 stays in the denominator
x^-4 in the denominator: -4 times -1 is +4; the x^4 stays in the denominator

My result is p^7, 3, q^2, and x^4 in the numerator, and 2 and z^3 in the denominator:

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