What is the simplified form of (-8x^4y^3)(-6xy^-7)?

What is the simplified form of (-8x^4y^3)(-6xy^-7)?

• A. 24x^3/y^4
• B. 48x^5/y^4
• C. 48x^3/y^4
• D. 24x^5/y^3

Answer: (B)

To simplify the expression (-8x^4y^3)(-6xy^-7), you start by multiplying the coefficients and then the variables. First, multiply the coefficients: - The coefficients are -8 and -6. When multiplied, they give you 48 because a negative times a negative yields a positive. Next, for the variable part, you will multiply the x terms and the y terms separately: 1. **For the x terms**: You have x^4 from the first term and x from the second term. When multiplying these, you apply the law of exponents which states that you add the exponents when multiplying like bases. Therefore, x^4 * x^1 = x^(4+1) = x^5. 2. **For the y terms**: You have y^3 from the first term and y^-7 from the second term. Similarly, you add the exponents: y^3 * y^-7 = y^(3 + (-7)) = y^(-4). To express y^(-4) in a simplified form, it can be rewritten as 1/y^4. Combining these results, you get: - Coefficient:

To simplify the expression (-8x^4y^3)(-6xy^-7), you start by multiplying the coefficients and then the variables.

First, multiply the coefficients:

• The coefficients are -8 and -6. When multiplied, they give you 48 because a negative times a negative yields a positive.

Next, for the variable part, you will multiply the x terms and the y terms separately:

1. For the x terms:

You have x^4 from the first term and x from the second term. When multiplying these, you apply the law of exponents which states that you add the exponents when multiplying like bases. Therefore, x^4 * x^1 = x^(4+1) = x^5.

2. For the y terms:

You have y^3 from the first term and y^-7 from the second term. Similarly, you add the exponents: y^3 * y^-7 = y^(3 + (-7)) = y^(-4). To express y^(-4) in a simplified form, it can be rewritten as 1/y^4.

Combining these results, you get:

• Coefficient: