Simplify: (3x2y)(2xy3) (b) Express your answer in index form

April 24, 2026Mathematics

ScanSolve AI Answer

April 24, 2026

Answer

$6x^3y^4$

You're on a roll — let's solve question 12.

12. (a) Simplify: $(3x^2y)(2xy^3)$

Step 1: Multiply the numerical coefficients. $3 \times 2 = 6$

Step 2: Multiply the terms with $x$ . Using the rule $x^a \cdot x^b = x^{a+b}$ : $x^2 \cdot x^1 = x^{2+1} = x^3$

Step 3: Multiply the terms with $y$ . Using the rule $y^a \cdot y^b = y^{a+b}$ : $y^1 \cdot y^3 = y^{1+3} = y^4$

Step 4: Combine the results. $(3x^2y)(2xy^3) = 6x^3y^4$ The simplified expression is $\boxed{6x^3y^4}$ .

12. (b) Express your answer in index form

The simplified expression from part (a) is already in index form, where variables are written with their exponents. The answer in index form is $\boxed{6x^3y^4}$ .

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You're on a roll — let's solve question 12. 12.

Asked on April 24, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

ScanSolve AI AnswerAnswered on April 24, 2026

You're on a roll — let's solve question 12. 12. (a) Simplify: (3x^2y)(2xy^3) Step 1: Multiply the numerical coefficients. 3 × 2 = 6 Step 2: Multiply the terms with x. Using the rule x^a · x^b = x^a+b: x^2 · x^1 = x^2+1 = x^3 Step 3: Multiply the terms with y. Using the rule y^a · y^b = y^a+b: y^1 · y^3 = y^1+3 = y^4 Step 4: Combine the results. (3x^2y)(2xy^3) = 6x^3y^4 The simplified expression is 6x^3y^4. 12. (b) Express your answer in index form The simplified expression from part (a) is already in index form, where variables are written with their exponents. The answer in index form is 6x^3y^4. What's next?