Answer:
The reason why a^4b^2 is not equal to (ab)^6 is because the exponents in each expression are applied differently.
Step-by-step explanation:
In the expression a^4b^2, the exponents 4 and 2 are only applied to their respective bases, which means a^4 is equal to a * a * a * a and b^2 is equal to b * b.
On the other hand, in the expression (ab)^6, the exponent 6 is applied to the entire quantity inside the parentheses, which is ab. This means (ab)^6 is equal to (ab) * (ab) * (ab) * (ab) * (ab) * (ab).
Let's simplify both expressions to see the difference:
a^4b^2 = (a * a * a * a) * (b * b) = a^4 * b^2
(ab)^6 = (ab) * (ab) * (ab) * (ab) * (ab) * (ab) = a^6 * b^6
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