How do you simplify #\frac { s ^ { 65} } { s ^ { - 1} \cdot s ^ { - 1} \cdot s }#?

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Answer 1 · 2017-12-04T04:14:53

See a solution process below:

First, use these rules of exponents to simplify the denominator:

#a = a^color(red)(1)# and #x^color(red)(a) xx x^color(blue)(b) = x^(color(red)(a) + color(blue)(b))#

#s^65/(s^-1 * s^-1 * s) =>#

#s^65/(s^color(red)(-1) * s^color(blue)(-1) * s^color(green)(1)) =>#

#s^65/s^(color(red)(-1)+color(blue)(-1)+color(green)(1)) =>#

#s^65/s^(color(red)(-1)-color(blue)(1)+color(green)(1)) =>#

#s^65/s^(-2+color(green)(1)) =>#

#s^65/s^-1#

Now, use this rule of exponents to complete the simplificcation:

#x^color(red)(a)/x^color(blue)(b) = x^(color(red)(a)-color(blue)(b))#

#s^color(red)(65)/s^color(blue)(-1) =>#

#s^(color(red)(65)-color(blue)(-1)) =>#

#s^(color(red)(65)+color(blue)(1)) =>#

#s^66#