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Simplify. Express your answer using positive exponents.\newlineq9q9q9\frac{q^9 \cdot q^{-9}}{q^9}

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Q. Simplify. Express your answer using positive exponents.\newlineq9q9q9\frac{q^9 \cdot q^{-9}}{q^9}
  1. Identify Operation: Identify the operation needed for the exponents.\newlineWhen we multiply powers with the same base, we add the exponents. When we divide powers with the same base, we subtract the exponents.
  2. Simplify Numerator: Simplify the numerator q9q9q^9 \cdot q^{-9}. We add the exponents because the bases are the same and we are multiplying. q9q9=q9+(9)=q0q^9 \cdot q^{-9} = q^{9 + (-9)} = q^0 Any number to the power of 00 is 11, so q0=1q^0 = 1.
  3. Divide by q9q^9: Divide the result from Step 22 by q9q^9. Since q0=1q^0 = 1, we have 1q9\frac{1}{q^9}. When we divide by a power, we subtract the exponents, but since the numerator is 11 (which is q0q^0), we have q09=q9q^{0 - 9} = q^{-9}. However, we need to express the answer with positive exponents.
  4. Express with Positive Exponent: Express q9q^{-9} with a positive exponent.\newlineA negative exponent means that the base is on the wrong side of the fraction line. To make the exponent positive, we can rewrite q9q^{-9} as 1/q91/q^{9}.

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