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Simplify. Express your answer using positive exponents. \newline6p(6p2)(p)\frac{6p}{(6p^2)(p)}

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Q. Simplify. Express your answer using positive exponents. \newline6p(6p2)(p)\frac{6p}{(6p^2)(p)}
  1. Identify Common Factors: Write down the given expression and identify the common factors in the numerator and the denominator.\newlineThe given expression is 6p(6p2)(p)\frac{6p}{(6p^2)(p)}. We can see that there is a common factor of 6p6p in the numerator and the denominator.
  2. Cancel Common Factors: Simplify the expression by canceling out the common factors. The 6p6p in the numerator and one of the pp's in the denominator will cancel out, as they are common factors. This leaves us with: 1p2(p)\frac{1}{p^2(p)}
  3. Combine Exponents: Combine the exponents in the denominator using the product rule of exponents.\newlineThe product rule states that when you multiply powers with the same base, you add the exponents. So we have:\newline1p2+1\frac{1}{p^{2+1}}\newline= 1p3\frac{1}{p^3}
  4. Final Simplified Expression: Write the final simplified expression using positive exponents.\newlineThe final simplified expression is 1p3\frac{1}{p^3}, which is already written with a positive exponent.

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