Final answer:
To simplify the expression 4xy³ ⋅ 7x²y³, multiply the coefficients (4 and 7) to get 28, and add the exponents of like bases, resulting in 28x³y⁶.
Step-by-step explanation:
To simplify the expression 4xy³ ⋅ 7x²y³ using properties of exponents, we can combine the coefficients and add the exponents of like bases. The coefficients 4 and 7 are multiplied together, and the variables x and y with their respective exponents are combined by adding exponents when the bases are the same. Here's how you simplify the expression step by step:
- Multiply the coefficients: 4 ⋅ 7 = 28.
- Add the exponents of x: x¹ ⋅ x² = x^(1+2) = x³.
- Add the exponents of y: y³ ⋅ y³ = y^(3+3) = y⁶.
Therefore, the simplified expression is 28x³y⁶.
To simplify the expression 4xy³ ∙ 7x²y³ using properties of exponents, we can apply the property of multiplication of exponents.
First, let's simplify the coefficients: 4 ∙ 7 = 28.
Then, let's simplify the variables with the same base (x and y) by adding their exponents: x^1 ∙ x^2 = x^(1+2) = x^3, and y^3 ∙ y^3 = y^(3+3) = y^6.
So, the simplified expression is 28x³y^6.