If ab ≠ 0, which of the following is equivalent to (8a * b ^ 7)(- 7a ^ - 5 * b ^ 2) ?

Rationale

-(56b⁹/a^4)

To simplify the expression (8a * b^7)(-7a^-5 * b^2), we first multiply the coefficients and then combine like terms for the variables. The final result after simplification is indeed -(56b⁹/a^4), which corresponds to option D.

A (b⁹/a^4) YOUR ANSWER

This option ignores the negative sign and the coefficient from the multiplication of 8 and -7. The correct calculation includes both, resulting in a negative coefficient of -56, which is not accounted for in this option.

B (-(8b⁹/7a^4)) YOUR ANSWER

While this option has the correct negative sign, it incorrectly applies the coefficients. The product of 8 and -7 should yield -56, not -8/7. Therefore, this expression does not match the correct simplification.

C (-(56b^14/a^5)) YOUR ANSWER

This option miscalculates the exponent for b and the exponent for a. The correct combination of exponents results in b^9 and a^-4, rather than b^14 and a^-5. Hence, this choice does not reflect the correct simplification.

D (-(56b⁹/a^4)) CORRECT

This is the correct answer because it correctly combines the coefficients (-56) and the variable exponents (b^9 and a^-4) from the multiplication of the two expressions.

E (-56a^5b^14) YOUR ANSWER

This option incorrectly represents the variables, showing a^5 and b^14. The correct simplification leads to a^-4 and b^9, making this option incorrect.

Conclusion

The expression (8a * b^7)(-7a^-5 * b^2) simplifies to -(56b⁹/a^4), confirming option D as the correct answer. Other choices fail due to inaccuracies in coefficients, variable exponents, or both, highlighting the importance of careful algebraic manipulation when simplifying expressions.

If ab ≠ 0, which of the following is equivalent to (8a * b ^ 7)(- 7a ^ - 5 * b ^ 2) ?

-(56b⁹/a^4)

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