Question

Multiply and simplify the following rational expression

Answer 1

Answer:

$\frac{3y^{4}}{5x}\textrm{ or }\frac{3}{5}x^{-1}y^{4}$

Step-by-step explanation:

The expression is:

$\frac{2x^{3}y^{6}}{5x^{2}y}\times \frac{15x^{2}}{10x^{4}y}$

First, we will multiply the numerators together and denominators together.

This gives,

$\frac{(2\times 15)(x^{3}\times x^{2})(y^{6})}{(5\times 10)(x^{2}\times x^{4})(y\times y)}$

Now, we use the exponent property $x^{a}\times x^{b}=x^{a+b}$.

This gives,

$\frac{30x^{3+2}y^{6}}{50x^{2+4}y^{2}}\\=\frac{30x^{5}y^{6}}{50x^{6}y^{2}}$

Now, we use the exponent property $\frac{x^{a}}{x^{b}}=x^{a-b}$

This gives,

$\frac{30x^{5}y^{6}}{50x^{6}y^{2}}=\frac{3}{5}x^{5-6}y^{6-2}=\frac{3}{5}x^{-1}y^{4}$

From the properties of exponents, $x^{-a}=\frac{1}{x^{a}}$

So, $\frac{3}{5}x^{-1}y^{4}=\frac{3y^{4}}{5x}$