Let's simplify the expression:

$\frac{4b^2 \times 2b^3}{8b}$

Step 1: Multiply the terms in the numerator

In the numerator, we have $4b^2 \times 2b^3$.

• Multiply the constants: $4 \times 2 = 8$.
• Use the law of exponents for the terms involving $b$: $b^2 \times b^3 = b^{2+3} = b^5$.

So, the expression in the numerator becomes:

$8b^5$

Step 2: Substitute back into the expression

Now we have:

$\frac{8b^5}{8b}$

Step 3: Simplify by dividing the terms

• The constant $8$ in the numerator and denominator cancels out.
• For the terms with $b$, we use the law of exponents: $\frac{b^5}{b} = b^{5-1} = b^4$.

Thus, the simplified form of the expression is:

$b^4$

Would you like further details on any step, or do you have any questions?

Here are some related questions for further practice:

1. How would you simplify $\frac{6a^3 \times 3a^2}{9a}$?
2. What is the result of $\frac{10x^4 \times 2x}{5x^3}$?
3. How can you simplify $\frac{7y^5 \times y^2}{y^3}$?
4. How do you approach simplifying $\frac{12m^3 \times 4m}{16m^2}$?
5. What would $\frac{15c^6}{5c^2}$ simplify to?

Tip: When simplifying expressions with exponents, remember to apply the laws of exponents carefully, especially when dividing terms with the same base.