Postsecondary Education Readiness Test (PERT) 2025 – 400 Free Practice Questions to Pass the Exam

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: