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Simplify. Express your answer using positive exponents.\newline2t2t9\frac{2t}{2t^9}

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Q. Simplify. Express your answer using positive exponents.\newline2t2t9\frac{2t}{2t^9}
  1. Write Expression: Write down the given expression.\newlineWe have the expression 2t2t9\frac{2t}{2t^9}, which is a fraction where the numerator is 2t2t and the denominator is 2t92t^9.
  2. Simplify Coefficients: Simplify the coefficients.\newlineThe coefficients 22 in the numerator and denominator cancel each other out because they are the same.\newline2t2t9=tt9\frac{2t}{2t^9} = \frac{t}{t^9}
  3. Apply Quotient Rule: Apply the quotient rule for exponents. The quotient rule states that when dividing like bases, you subtract the exponents. tt9=t19=t8\frac{t}{t^9} = t^{1-9} = t^{-8}
  4. Express Answer: Express the answer using positive exponents.\newlineSince the question prompt asks for positive exponents, we need to rewrite t8t^{-8} as 1/t81/t^8.\newlinet8=1/t8t^{-8} = 1/t^8