Simplify:
[tex](6r^4s^3)(9rs^2)[/tex]
Answer (2)
To simplify the expression ( 6 r 4 s 3 ) ( 9 r s 2 ), multiply the coefficients to get 54 and add the exponents of like bases to get r 5 and s 5 , resulting in 54 r 5 s 5 .
To simplify the expression ( 6 r 4 s 3 ) ( 9 r s 2 ) , you need to apply the associative property of multiplication to combine like terms. The rule states that when multiplying powers with the same base, you add the exponents.
Step 1: Multiply the coefficients (numbers in front of the variables): 6 × 9 = 54.
Step 2: Combine the r terms using the rule for exponents (add the exponents): r 4 × r = r ( 4 + 1 ) = r 5 .
Step 3: Combine the s terms using the rule for exponents: s 3 × s 2 = s ( 3 + 2 ) = s 5 .
Thus, the simplified expression is 54 r 5 s 5 .
To simplify ( 6 r 4 s 3 ) ( 9 r s 2 ) , multiply the coefficients to get 54. Then, add the exponents of like bases to obtain r 5 and s 5 . The final simplified expression is 54 r 5 s 5 .
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