How do you simplify #(\frac { - 5x ^ { 2} y ^ { 5} } { x ^ { 4} y } ) ^ { 3}#?

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Answer 1 · 2017-10-05T23:42:52

#(-125y^12)/x^6#

You can simplify this question using properties of exponents so it looks like this:

#(-5x^2y^5)^3/(x^4y)^3#

Then looking just at the numerator, we expand it out. Taking this to the power of 3 means we must multiply it by itself 3 times.

So #(-5x^2y^5)^3 = (-5x^2y^5)(-5x^2y^5)(-5x^2y^5)#

If you look at it by parts here, #-5*-5*-5=-125#

#x^2*x^2*x^2=x^6# and #y^5*y^5*y^5=y^15#

So, #(-5x^2y^5)(-5x^2y^5)(-5x^2y^5) = -125x^6y^15#

Doing the same process with the denominator we get #x^12y^3#

If we divide these two expressions we have to subtract the exponents so we end up with #-125x^-6y^12#

Finally negative exponents can be written positive if you flip it from the numerator to the denominator (or vice versa) so:

#-125x^-6y^12=(-125y^12)/x^6#