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Simplify. Express your answer using a single exponent.\newline(z3)−4(z^{3})^{-4}

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Full solution

Q. Simplify. Express your answer using a single exponent.\newline(z3)−4(z^{3})^{-4}
  1. Understand Rule: Understand the exponent rule for powers raised to powers.\newlineWhen you have a power raised to another power, you multiply the exponents.
  2. Apply to Expression: Apply the exponent rule to (z3)−4(z^3)^{-4}. We multiply the exponents 33 and −4-4. (z3)−4=z(3×−4)(z^3)^{-4} = z^{(3 \times -4)}
  3. Perform Exponent Multiplication: Perform the multiplication of the exponents.\newlineCalculate 3×−43 \times -4 to get −12-12.\newlinez3×−4=z−12z^{3 \times -4} = z^{-12}
  4. Express Answer Positively: Express the answer using a positive exponent.\newlineSince the problem asks for a positive exponent, we need to take the reciprocal of the base to make the exponent positive.\newlinez−12=1z12z^{-12} = \frac{1}{z^{12}}

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