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Simplify. Express your answer using positive exponents.\newline8z4z5\frac{8z}{4z^5}

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Full solution

Q. Simplify. Express your answer using positive exponents.\newline8z4z5\frac{8z}{4z^5}
  1. Simplify Coefficients: Simplify the coefficients.\newlineDivide the coefficients 88 by 44.\newline84=2\frac{8}{4} = 2
  2. Simplify Variables with Exponents: Simplify the variables with exponents.\newlineDivide zz by z5z^5 using the property of exponents am/an=a(m−n)a^m / a^n = a^{(m-n)}.\newlinez/z5=z(1−5)=z−4z / z^5 = z^{(1-5)} = z^{-4}
  3. Express with Positive Exponents: Express the answer with positive exponents.\newlineSince we cannot have negative exponents in the final answer, we rewrite z−4z^{-4} as 1/z41/z^4.\newline2⋅z−4=2/z42 \cdot z^{-4} = 2 / z^4
  4. Combine Results: Combine the results from Step 11 and Step 33.\newlineThe simplified expression is 2/z42 / z^4.

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