Write Problem and Factor: Write down the multiplication problem and factor out any common factors in the numerators and denominators. 10np6n2×9n2 can be factored as (10×n×p6×n2)×(9×n2).
Cancel Common Factors: Cancel out any common factors in the numerator and denominator. The n in the denominator cancels with one n from n2 in the numerator, and the numbers 6 and 10 can be simplified by dividing both by their greatest common factor, which is 2. This gives us (3×n×n2)/(5×p)×(9×n2).
Multiply Numerators and Denominators: Multiply the numerators together and the denominators together.(3×n×n2×9×n2)/(5×p) simplifies to (3×9×n4×n2)/(5×p).
Simplify Constants and Combine Terms: Simplify the multiplication of the constants and combine the n terms by adding their exponents.(3×9)=27 and n4×n2=n(4+2)=n6. So, the expression simplifies to 5p27n6.
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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