How do you simplify $((-7^2 r^5 s^-3)/( 3^-1 r^-4 s^4))^4$ ?

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Answer 1 · 2015-07-11T23:04:44

$A=((147^4)*r^36)/(s^28)$

Let's go to simplify : $A=((-7^2r^5s^(-3))/(3^(-1)r^(-4)s^4))^4$

First, use this properties :
$->$ $color(red)(a^(-n) = 1/a^n)$
$->$ $color(red)(1/a^(-n) = a^n)$

$A=((-7^2*color(red)(3^1)r^5color(red)(r^4))/(s^4color(red)(s^3)))^4$

Second, simplify $A$ with that :

$color(blue)(a^n*a^m=a^(n+m))$

$A=((-49*3*color(blue)(r^9))/(color(blue)(s^7)))^4$

Finally, apply the power $4$ to the fraction inside the parenthesis, with :

$color(green)((kxxa^x)^y=k^yxxa^(x*y))$

$A=((-147)^4*color(green)(r^36))/(color(green)(s^28))$

Therefore :

$A=(466948881*r^36)/(s^28)$

How do you simplify ((-7^2 r^5 s^-3)/( 3^-1 r^-4 s^4))^4((-7^2 r^5 s^-3)/( 3^-1 r^-4 s^4))^4?