  ### Home > CCA2 > Chapter B > Lesson B.1.6 > ProblemB-73

B-73.

Jack and Jill were working on simplifying the expression below, but they were having some trouble. Then Jill had an idea.

$\frac { 3 x ^ { 2 } y ^ { - 3 } } { x ^ { - 1 } y ^ { 2 } }$

“Can’t we separate the parts?” she said. “That way, it might be easier to tell what we can simplify.” She rewrote the expression as shown below.

$3\cdot x^2\cdot\frac{1}{x^{-1}}\cdot y^{-3}\cdot\ \frac{1}{y^2}$

“Okay,” said Jack. “Now we can rewrite each of the parts with negative exponents and simplify.”  Homework Help ✎

1. Help Jack and Jill finish simplifying their expression.

Notice that Jill used the Associative Property and put the factors with the same variables next to each other.

Remember, $\frac{1}{x^{-1}}=x$. What does $y^{-3}$ equal?

$\frac{3x^3}{y^5}$

2. Use their idea to rewrite and simplify $\frac { m ^ { 2 } p q ^ { - 1 } } { 4 m ^ { - 2 } p q ^ { 3 } }$.

$\frac{1}{4}\cdot m^2\cdot\frac{1}{m^{-2}}\cdot p\cdot\frac{1}{p}\cdot q^{-1}\cdot\frac{1}{q^3}$