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Multiply. Simplify your answer.\newline6n210np×9n2\frac{6n^2}{10np} \times 9n^2

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Q. Multiply. Simplify your answer.\newline6n210np×9n2\frac{6n^2}{10np} \times 9n^2
  1. Write Problem and Factor: Write down the multiplication problem and factor out any common factors in the numerators and denominators. 6n210np×9n2\frac{6n^2}{10np} \times 9n^2 can be factored as (6×n210×n×p)×(9×n2)\left(\frac{6 \times n^2}{10 \times n \times p}\right) \times (9 \times n^2).
  2. Cancel Common Factors: Cancel out any common factors in the numerator and denominator. The nn in the denominator cancels with one nn from n2n^2 in the numerator, and the numbers 66 and 1010 can be simplified by dividing both by their greatest common factor, which is 22. This gives us (3×n×n2)/(5×p)×(9×n2)(3 \times n \times n^2)/(5 \times p) \times (9 \times n^2).
  3. Multiply Numerators and Denominators: Multiply the numerators together and the denominators together.\newline(3×n×n2×9×n2)/(5×p)(3 \times n \times n^2 \times 9 \times n^2) / (5 \times p) simplifies to (3×9×n4×n2)/(5×p)(3 \times 9 \times n^4 \times n^2) / (5 \times p).
  4. Simplify Constants and Combine Terms: Simplify the multiplication of the constants and combine the nn terms by adding their exponents.(3×9)=27(3 \times 9) = 27 and n4×n2=n(4+2)=n6n^4 \times n^2 = n^{(4+2)} = n^6. So, the expression simplifies to 27n65p\frac{27n^6}{5p}.
  5. Check Further Simplification: Check for any further simplification. Since there are no common factors left between the numerator and the denominator, the expression is already in its simplest form.

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