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Simplify. Express your answer using positive exponents. \newline2z2z9\frac{2z}{2z^9}

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Full solution

Q. Simplify. Express your answer using positive exponents. \newline2z2z9\frac{2z}{2z^9}
  1. Write Expression: Write down the given expression.\newlineWe have the expression 2z2z9\frac{2z}{2z^9}.
  2. Simplify Coefficients and Exponents: Simplify the expression by dividing the coefficients and subtracting the exponents.\newlineSince the bases are the same zz, we can divide the coefficients 22\frac{2}{2} and subtract the exponents 1−91 - 9 for zz.\newline2z2z9=(22)×z(1−9)\frac{2z}{2z^9} = \left(\frac{2}{2}\right) \times z^{(1-9)}
  3. Calculate Division and Subtraction: Calculate the division of the coefficients and the subtraction of the exponents.\newline(22)=1(\frac{2}{2}) = 1\newlinez(1−9)=z−8z^{(1-9)} = z^{-8}
  4. Rewrite Negative Exponent: Since we need to express the answer using positive exponents, we rewrite z−8z^{-8} as 1/z81/z^8.\newline1×z−8=1/z81 \times z^{-8} = 1/z^8
  5. Combine Results: Combine the results to get the final simplified expression. 2z2z9=1z8\frac{2z}{2z^9} = \frac{1}{z^8}

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