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Simplify. Express your answer using positive exponents.\newline10z2z5\frac{10z}{2z^5}

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Full solution

Q. Simplify. Express your answer using positive exponents.\newline10z2z5\frac{10z}{2z^5}
  1. Simplify Coefficients and Exponents: Simplify the expression by dividing the coefficients and subtracting the exponents of like bases.\newline10z2z5=102⋅z1z5\frac{10z}{2z^5} = \frac{10}{2} \cdot \frac{z^1}{z^5}
  2. Calculate Division and Simplify Powers: Calculate the division of the coefficients and simplify the powers of zz.10/2=510 / 2 = 5, and z1/z5=z(1−5)=z−4z^1 / z^5 = z^{(1-5)} = z^{-4}
  3. Express Final Answer: Express the final answer using positive exponents by writing z−4z^{-4} as 1/z41/z^4.\newline5⋅z−4=5/z45 \cdot z^{-4} = 5 / z^4

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