4a³b×(3ab)²
4a³b×(3ab)²
= (4a^3 b)(9a^2 b^2)
= 36 a^5 b^3
To simplify the expression 4a³b×(3ab)², we need to apply the rules of exponents and perform the necessary calculations step-by-step.
1. Start by simplifying the expression inside the parentheses, (3ab)². To square a binomial, we need to multiply it by itself:
(3ab)² = (3ab) × (3ab) = 9a²b²
2. Now we can substitute the simplified expression back into the original expression:
4a³b × 9a²b²
3. Multiply the numerical coefficients: 4 × 9 = 36
4. Multiply the variables with the same base by adding their exponents: a³ × a² = a^(3+2) = a⁵, and b × b² = b^(1+2) = b³
5. Substitute the results back into the expression:
36a⁵b³
To simplify the expression 4a³b×(3ab)², we can use the rules of exponents and multiplication.
Let's break it down step by step:
Step 1: Simplify the expression inside the parentheses.
(3ab)² means to square the quantity 3ab.
(3ab)² = (3ab) × (3ab)
= 9a²b² (multiplying the terms inside the parentheses)
Step 2: Multiply the result from Step 1 with 4a³b.
4a³b×(3ab)² = 4a³b × 9a²b²
To multiply the terms, we need to multiply the coefficients (constants) and combine the variables.
Step 3: Multiply the coefficients: 4 × 9 = 36.
Step 4: Multiply the variables:
- For the variable 'a', we add the exponents: a³ × a² = a³+² = a^(3+2) = a⁵.
- For the variable 'b', we add the exponents: b × b² = b¹+² = b³.
Putting it all together, we get:
4a³b × 9a²b² = 36a⁵b³
So, the simplified expression is 36a⁵b³.