How do you simplify \frac { z y ^ { 5} } { z ^ { 7} y ^ { 3} }?

2 Answers
Jul 31, 2017

Expression = (y/z^3)^2

Explanation:

Here we will use three rules of exponents as follows:

(i) 1/a = a^-1

(ii) a^mxxa^n = a^(m+n)

(iii) (a^m)^n = a^(mxxn)

Expression = (zy^5)/(z^7y^3)

= z^1/z^7 xx y^5/y^3

Apply (i) & (ii)

= z^(1-7) xx y^(5-3)

= z^-6 xx y^2

Reverse (i)

= y^2 xx 1/z^6 = y^2/z^6

Apply (iii)

= (y/z^3)^2

Jul 31, 2017

y^2/z^6 or y^2z^-6

Explanation:

A] One way is to subtract the smaller exponent from the larger exponent of the same number.

(zy^5)/(z^7y^3)=(y^(5-3))/(z^(7-1))=y^2/z^6=y^2z^-6

B] Another way is to expand the exponents and cancel the common ones in the numerator and denominator.

(z*y*y*y*y*y)/(z*z*z*z*z*z*z*y*y*y)=(cancelz*cancely*cancely*cancely*y*y)/(cancelz*z*z*z*z*z*z*cancely*cancely*cancely)=(y*y)/(z*z*z*z*z*z)=y^2/z^6

We can write this as y^2/z^6 or bring the denominator up by changing the exponent into a negative.

y^2z^-6