Postsecondary Education Readiness Test (PERT) Practice Test

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

  1. 24x^3/y^4

  2. 48x^5/y^4

  3. 48x^3/y^4

  4. 24x^5/y^3

The correct answer is: 48x^5/y^4

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: