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Answer:
[tex]\frac{12a^3b^6c^5}{3a^2b^4c^5}=4ab^{2}[/tex]
Step-by-step explanation:
Given
[tex]\frac{12a^3b^6c^5}{3a^2b^4c^5}[/tex]
Required
Simplify
[tex]\frac{12a^3b^6c^5}{3a^2b^4c^5}[/tex]
To solve this, we apply the following law of indices:
[tex]\frac{m^x}{m^y} = m^{x-y}[/tex]
[tex]\frac{12a^3b^6c^5}{3a^2b^4c^5}[/tex] becomes
[tex]\frac{12}{3}a^{3-2}b^{6-4}c^{5-5}[/tex]
[tex]\frac{12}{3}a^{1}b^{2}c^{0}[/tex]
[tex]c^0 = 1[/tex]; So, we have
[tex]\frac{12}{3}a^{1}b^{2}*1[/tex]
Finally,
[tex]4ab^{2}[/tex]
Hence:
[tex]\frac{12a^3b^6c^5}{3a^2b^4c^5}=4ab^{2}[/tex]