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Simplify. Express your answer using a single exponent.\newline(z−5)−3(z^{-5})^{-3}

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Full solution

Q. Simplify. Express your answer using a single exponent.\newline(z−5)−3(z^{-5})^{-3}
  1. Understand the problem: Understand the problem.\newlineWe need to simplify the expression (z−5)−3(z^{-5})^{-3} by using the power of a power rule, which states that (am)n=am∗n(a^{m})^{n} = a^{m*n}.
  2. Apply power of power rule: Apply the power of a power rule.\newline(z−5)−3(z^{-5})^{-3} can be simplified by multiplying the exponents −5-5 and −3-3 together.\newlineSo, (z−5)−3=z(−5⋅−3).(z^{-5})^{-3} = z^{(-5 \cdot -3)}.
  3. Perform exponent multiplication: Perform the multiplication of the exponents.\newlineNow we calculate −5×−3-5 \times -3 which equals 1515.\newlineSo, z(−5×−3)=z15z^{(-5 \times -3)} = z^{15}.
  4. Write final answer: Write the final answer.\newlineThe expression (z−5)−3(z^{-5})^{-3} simplifies to z15z^{15}.

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