Answer:
The expression [tex]\left(\frac{a^3b^2c}{a^5c^2}\right)\left(\frac{a^2b}{c^4}\right)[/tex] is equal to [tex]\frac{b^3}{c^5}[/tex]
Step-by-step explanation:
We have the following expression
[tex]\left(\frac{a^3b^2c}{a^5c^2}\right)\left(\frac{a^2b}{c^4}\right)[/tex]
To simplify the expression you need to:
The left side of the expression is [tex]\frac{a^3b^2c}{a^5c^2}=\frac{b^2}{a^2c}[/tex] because
[tex]\mathrm{Apply\:exponent\:rule}:\quad \frac{x^a}{x^b}=\frac{1}{x^{b-a}}[/tex]
[tex]\frac{a^3}{a^5}=\frac{1}{a^{5-3}}[/tex] and [tex]\frac{c}{c^2}=\frac{1}{c^{2-1}}[/tex]
[tex]\frac{b^2}{c^{2-1}a^{5-3}} = \frac{b^2}{a^2c}[/tex]
Next,
[tex]\frac{a^2b}{c^4}\cdot \frac{b^2}{a^2c}[/tex]
[tex]\mathrm{Multiply\:fractions}:\quad \frac{a}{b}\cdot \frac{c}{d}=\frac{a\:\cdot \:c}{b\:\cdot \:d}[/tex]
[tex]\frac{b^2a^2b}{a^2cc^4}[/tex]
[tex]\mathrm{Cancel\:the\:common\:factor:}\:a^2[/tex]
[tex]\frac{b^2b}{cc^4}[/tex]
We know that [tex]b^2b=b^3[/tex] and [tex]cc^4=c^5[/tex]
Therefore [tex]\frac{b^3}{c^5}[/tex]
