Question

Simplify, showing your steps. Tell the property you used in each step.

(3/2x)(2/3y)

Simplify, showing your steps. Tell the property you used in each step.

(3/2x)(2/3y)

@Mathematics

Answer 1

1/xy

Answer 2

\[\frac{3}{2x} * \frac{2}{3y}\]
=\[3*(2x)^{-1} * 2 * (3y)^{-1} \ \ \ \ \text{just rewriting stuff...} a/b = a * b^{-1}\]
\[= 3 * 2^{-1}*x^{-1} * 2 * 3 ^{-1} * y^{-1}\ \ \ \ (ab)^{-1} = a^{-1}b^{-1}; \text{a and b are non-zero integers}\]
\[=3*3^{-1} * 2 * 2^{-1} * x^{-1} * y^{-1} \ \ \ \ \text{commutative property of multiplication}\]
\[=x^{-1} * y^{-1}\ \ \ \ \ \text{property of multiplicative inverse}\]then just rewrite that as \[\frac{1}{xy}\]

Answer 3

you can go practice your skills on my next one? haha, I did it, just double checking my answers