How do you simplify #\frac { 3y ^ { - 2} } { ( 2y ) ^ { 3} }#?

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Answer 1 · 2017-01-02T02:54:21

First, expand the term in the denominator and then factor the numerator and denominator using the rules for exponents.

Step 1) Expand the term in the denominator using the following rule for exponents:

#color(red)((x^a)^b = x^(a*b))# and

#color(red)(x =x^1)#

#(3y^-2)/(2^3y^(1*3))#

#(3y^-2)/(8y^3)#

We can now simplify the #y# terms using this rule for exponents:

#color(red)(x^a/x^b = 1/x^(b-a))#

#3/(8y^(3- -2)#

#3/(8y^5)#