1. $$ (a)(-3 a)\left(a^{2}\right) $$

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$$ -3a^4. $$ To simplify the expression $$ (a)(-3a)(a^2) $$, we can follow these steps: 1. **Multiply the coefficients**: The coefficients are $$1$$ (from $$a$$) and $$-3$$ (from $$-3a$$). So, $$1 \times -3 = -3$$. 2. **Combine the variables**: When multiplying variables with the same base, we add their exponents. The exponents of $$a$$ in the expression are: - $$a$$ has an exponent of $$1$$ (since $$a = a^1$$), - $$-3a$$ has an exponent of $$1$$, - $$a^2$$ has an exponent of $$2$$. Therefore, we add the exponents: $$ 1 + 1 + 2 = 4. $$ 3. **Combine the results**: Now we can combine the coefficient and the variable: $$ -3a^4. $$ Thus, the simplified expression is: $$ \boxed{-3a^4}. $$

1. \( (a)(-3 a)\left(a^{2}\right) \)

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1. \( (a)(-3 a)\left(a^{2}\right) \)

UpStudy ThothAI Solution

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