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Simplify. Express your answer using positive exponents. \newline6w73w8\frac{6w^7}{3w^8}

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Q. Simplify. Express your answer using positive exponents. \newline6w73w8\frac{6w^7}{3w^8}
  1. Identify Coefficients and Powers: Identify the coefficients and the powers of ww in the expression.\newlineWe have the coefficient 66 in the numerator and 33 in the denominator. We also have ww raised to the power of 77 in the numerator and ww raised to the power of 88 in the denominator.
  2. Simplify Coefficients: Simplify the coefficients by dividing 66 by 33. 66 divided by 33 equals 22.
  3. Apply Quotient Rule: Apply the quotient rule for exponents to simplify w7/w8w^7/w^8. The quotient rule states that when dividing like bases, you subtract the exponents. w7/w8=w78=w1w^7/w^8 = w^{7-8} = w^{-1}.
  4. Rewrite Negative Exponent: Since we want to express the answer using positive exponents, we rewrite w1w^{-1} as 1w1\frac{1}{w^1} or simply 1w\frac{1}{w}.
  5. Combine Results: Combine the results from Step 22 and Step 44 to write the final simplified expression.\newlineThe final answer is 2×(1w)2 \times \left(\frac{1}{w}\right) or simply 2w.\frac{2}{w}.