Final answer:
The given mathematical expression, (-15v⁴x⁶+24v²x⁶)(-4v³x⁴), is simplified by dividing each term by (-4v³x⁴) and applying the rules of exponents, resulting in 3.75vx² - 6v⁻¹x².
Step-by-step explanation:
The given expression, (-15v⁴x⁶+24v²x⁶)(-4v³x⁴), can be simplified by dividing each term in the parentheses by (-4v³x⁴) and applying the rules of exponents which state that when dividing with the same bases, the exponents subtracted.
Divide -15v⁴ by -4v³ and subtract the exponents to get 3.75v. Divide x⁶ by x⁴ and subtract the exponents to get x². Do the same for the second term. Divide 24v² by -4v³ and x⁶ by x⁴. This will result in -6v⁻¹x².
So the simplified expression is 3.75vx² - 6v⁻¹x².
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