Question

Simplify ((x⁻⁴y⁻³z⁴ / (xy)⁻³z⁰))⁻⁴ completely and write your answer without negative exponents.

Answer 1

To simplify and remove the negative exponents from the given expression step-by-step, we can apply the laws of exponentiation. The result is x^4 / z^16.

Step-by-step explanation:

To simplify the expression (((x-4y-3z4) / (xy)-3z0))-4 and remove the negative exponents, we can apply the rules of exponentiation. Let's break it down step-by-step:

1. First, simplify the expression inside the parentheses. Use the rule (a / b)c = ac / bc.
2. (((x-4y-3z4) / (xy)-3z0))-4 = ((x-4y-3z4)-4) / ((xy)-3z0)-4
3. Next, apply the rule (ab)c = ab * c. Raise each term inside the parentheses to the power of -4.
4. ((x-4y-3z4)-4) / ((xy)-3z0)-4 = (x(-4 * -4)y(-3 * -4)z(4 * -4)) / (x(-3 * -4)y(-3 * -4)z(0 * -4))
5. Simplify the exponents.
6. (x16y12z-16) / (x12y12) = (x16-12y12-12z-16-0)
7. Finally, simplify further. x16-12 = x4 and z-16-0 = z-16.
8. (x4y0z-16) = x4 / z16

The simplified expression is x4 / z16. We have removed all negative exponents and obtained the final answer.

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