# How do you simplify (525x^5y^4w )/(630 x^4y^5z)?

Apr 24, 2018

$\frac{5 x w}{6 y z}$

#### Explanation:

Given: $\frac{525 {x}^{5} {y}^{4} w}{630 {x}^{4} {y}^{5} z}$

One way to simplify is to use the exponent rules:

${x}^{m} / {x}^{n} = {x}^{m - n} \text{ and } {x}^{-} 1 = \frac{1}{x}$

$\frac{525 {x}^{5} {y}^{4} w}{630 {x}^{4} {y}^{5} z} = \frac{5 {x}^{5 - 4} {y}^{4 - 5} w}{6 z} = \frac{5 x {y}^{-} 1 w}{6 z} = \frac{5 x w}{6 y z}$

A second way is to find the greatest common factor (GCF) in both the numerator and the denominator and cancel:

$525 {x}^{5} {y}^{4} w = 3 \cdot 5 \cdot 5 \cdot 7 \cdot x \cdot x \cdot x \cdot x \cdot x \cdot y \cdot y \cdot y \cdot y \cdot w$

$630 {x}^{4} {y}^{5} z = 2 \cdot 3 \cdot 3 \cdot 5 \cdot 7 \cdot x \cdot x \cdot x \cdot x \cdot y \cdot y \cdot y \cdot y \cdot y \cdot w$

GCF = $3 \cdot 5 \cdot 7 \cdot x \cdot x \cdot x \cdot x \cdot y \cdot y \cdot y \cdot y = 105 {x}^{4} {y}^{4}$

Factor using the GCF and cancel:

$\frac{525 {x}^{5} {y}^{4} w}{630 {x}^{4} {y}^{5} z} = \frac{\cancel{105 {x}^{4} {y}^{4}} \left(5 x w\right)}{\cancel{105 {x}^{4} {y}^{4}} \left(6 y z\right)} = \frac{5 x w}{6 y z}$