Answer:
[tex]\frac{27a^9 * 18b^5 * 4c^2 }{18a^4 * 12b^2 * 2c} = \frac{9}{2}a^5b^3c[/tex]
Step-by-step explanation:
Given
[tex]\frac{27a^9 * 18b^5 * 4c^2 }{18a^4 * 12b^2 * 2c}[/tex]
Required
Simplify
[tex]\frac{27a^9 * 18b^5 * 4c^2 }{18a^4 * 12b^2 * 2c}[/tex]
Cancel out 18
[tex]\frac{27a^9 * b^5 * 4c^2 }{a^4 * 12b^2 * 2c}[/tex]
Divide 4 and 2
[tex]\frac{27a^9 * b^5 * 2c^2 }{a^4 * 12b^2 *c}[/tex]
Divide 27 and 12 by 3
[tex]\frac{9a^9 * b^5 * 2c^2 }{a^4 * 4b^2 *c}[/tex]
Apply law of indices
[tex]\frac{9a^{9-4} * b^{5-2} * 2c^{2-1} }{4}[/tex]
[tex]\frac{9a^5 * b^3 * 2c }{4}[/tex]
Divide 2 and 4
[tex]\frac{9a^5 * b^3 * c}{2}[/tex]
[tex]\frac{9a^5b^3c}{2}[/tex]
Rewrite as:
[tex]\frac{9}{2}a^5b^3c[/tex]
Hence:
[tex]\frac{27a^9 * 18b^5 * 4c^2 }{18a^4 * 12b^2 * 2c} = \frac{9}{2}a^5b^3c[/tex]
