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Simplify. Express your answer using positive exponents.\newline9z9z3\frac{9z}{9z^3}

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Q. Simplify. Express your answer using positive exponents.\newline9z9z3\frac{9z}{9z^3}
  1. Write Expression: Write down the expression to be simplified.\newlineThe expression given is 9z9z3\frac{9z}{9z^3}. We need to simplify this expression by dividing the terms.
  2. Divide Coefficients and Variables: Divide the coefficients and the variables separately.\newlineSince the coefficients are the same 99\frac{9}{9}, they will divide out to 11. For the variables, we use the rule of exponents that states when dividing like bases, you subtract the exponents.
  3. Perform Coefficient Division: Perform the division of the coefficients. 99=1\frac{9}{9} = 1
  4. Subtract Exponents: Subtract the exponents of the variable zz. z1z3=z13=z2\frac{z^1}{z^3} = z^{1-3} = z^{-2}
  5. Rewrite Negative Exponent: Since we need to express the answer using positive exponents, we rewrite z2z^{-2} as 1/z21/z^2.
  6. Combine Results: Combine the results from Step 33 and Step 55.\newline1×1z2=1z21 \times \frac{1}{z^2} = \frac{1}{z^2}

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