# How do you simplify (16x^2)/y^4* (5x^2)/y^2?

Aug 8, 2015

=color(blue)(80 * x^(4)* y^(-6)

#### Explanation:

$\left(\frac{16 {x}^{2}}{y} ^ 4\right) \cdot \left(\frac{5 {x}^{2}}{y} ^ 2\right)$

• By property color(blue)(1/a = a^-1
Applying the above property to exponents of $y$ in the denominator.

$= 16 {x}^{2} {y}^{-} 4 \cdot 5 {x}^{2} {y}^{-} 2$

$= \left(16 \cdot 5\right) \cdot \left({x}^{2} \cdot {x}^{2}\right) \cdot \left({y}^{-} 4 \cdot {y}^{-} 2\right)$

• As per property
color(blue)(a^m *a^n = a^(m+n)

Applying the same property to the exponents of $x$ and $y$ in the expression
$= 80 \cdot \left({x}^{2 + 2}\right) \cdot \left({y}^{- 4 - 2}\right)$

=color(blue)(80 * x^(4)* y^(-6)