How do you simplify #((5x^2)/x^-4)^-2#?

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Answer 1 · 2016-09-06T05:44:26

#1 / (25 x^(12))#

We have: #((5 x^(2)) / (x^(- 4)))^(- 2)#

Using the laws of exponents:

#= (((5 x^(2))^(- 2)) / ((x^(- 4))^(- 2)))#

#= (5^(- 2) cdot x^(- 4)) / (x^(8))#

#= 5^( - 2) cdot x^(- 4 - 8)#

#= 5^(- 2) cdot x^(- 12)#

#= (1) / (5^(2) cdot x^(12))#

#= 1 / (25 x^(12))#

Answer 2 · 2016-09-06T06:25:15

#1/(25x^12)#

Recall: The law of indices : #(a/b)^-m = (b/a)^m#

This shows that a fraction raised to a negative index can be inverted and the index becomes positive.

I prefer to sort out the negative indices first.

#((5x^2)/x^-4)^color(red)(-2) = (x^-4/(5x^2))^color(red)(2)#

=# (color(blue)(x^-4)/(5x^2))^(2) = (1/(5x^2xx color(blue)(x^4)))^2#

=#(1/(5x^6))^2#

=#1/(25x^12)#