3.1. Simplify 3.1.1. $$ 2\left(4 x^{3}\right. $$ 3.1.2. $$ \frac{16 a^{4} b^{5}}{4 a^{3} b^{2}} $$

Question

UpStudy AI · Accepted Answer

**Problem 3.1.1**

Simplify the expression:
$$
2\left(4x^3\right)
$$

*Step 1:* Multiply the constant $$2$$ by $$4$$:
$$
2 \times 4 = 8
$$

*Step 2:* Attach the variable part $$x^3$$:
$$
8x^3
$$

Thus, the simplified expression is:
$$
8x^3
$$

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**Problem 3.1.2**

Simplify the expression:
$$
\frac{16a^4b^5}{4a^3b^2}
$$

*Step 1:* Simplify the numerical coefficients:
$$
\frac{16}{4} = 4
$$

*Step 2:* Simplify the $$a$$ terms using the law of exponents:
$$
\frac{a^4}{a^3} = a^{4-3} = a
$$

*Step 3:* Simplify the $$b$$ terms:
$$
\frac{b^5}{b^2} = b^{5-2} = b^3
$$

*Step 4:* Combine all the simplified parts:
$$
4 \cdot a \cdot b^3 = 4ab^3
$$

Thus, the simplified expression is:
$$
4ab^3
$$
**Simplified Answers:** 1. $$ 2(4x^3) = 8x^3 $$ 2. $$ \frac{16a^4b^5}{4a^3b^2} = 4ab^3 $$

3.1. Simplify 3.1.1. \( 2\left(4 x^{3}\right. \) 3.1.2. \( \frac{16 a^{4} b^{5}}{4 a^{3} b^{2}} \)