Final answer:
To simplify the given expression, divide each term separately using the rules of exponents, and combine the variables by subtracting their exponents. The answer is option A) (4x^4)/(3yz^3).
Step-by-step explanation:
To simplify the expression (8x^3y^-2z^-4)/(6x^-1yz^-5), we need to use the rules of exponents. First, we can simplify the coefficients: 8/6 = 4/3. Next, we can use the rule x^a / x^b = x^(a-b) to combine the x terms: x^3 / x^(-1) = x^(3-(-1)) = x^4. Similarly, we can combine the y terms: y^(-2) / y^1 = y^(-2-1) = y^-3. Finally, we can combine the z terms: z^(-4) / z^(-5) = z^(-4-(-5)) = z^1 = z. Putting it all together, the simplified expression is (4x^4)/(3yz^3). Therefore, option A) (4x^4)/(3yz^3) is the correct answer.
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