How would I solve these?

1. \[ (-3xy)^3 (-x^3) \]

2. \[ (-9b^2a^3)^2 (3^3b)^2 \]

( − 9 b 2 a 3 ) 2 ⋅ ( 3 3 b ) 2 = ( − 9 ) 2 ⋅ ( b 2 ) 2 ⋅ ( a 3 ) 2 ⋅ ( 3 3 ) 2 ⋅ ( b ) 2 = = 81 ⋅ b 4 ⋅ a 6 ⋅ 3 6 ⋅ b 2 = 3 4 ⋅ a 6 ⋅ b 4 ⋅ 3 6 ⋅ b 2 = = 3 4 + 6 \cdota 6 ⋅ b 4 + 2 = 3 10 ⋅ a 6 ⋅ b 6

Answered by Lilith | 2024-06-10

( − 3 x y ) 3 ( − x 3 ) = ( − 3 ) 3 x 3 y 3 ⋅ ( − x 3 ) = − 27 x 3 y 3 ⋅ ( − x 3 ) = 27 x 6 y 3 ( − 9 b 2 a 3 ) 2 ⋅ ( 3 3 b 2 ) 2 = ( − 3 2 a 3 b 2 ) 2 ⋅ ( 3 3 b 2 ) 2 = 3 2 ⋅ 2 a 3 ⋅ 2 b 2 ⋅ 2 ⋅ 3 3 ⋅ 2 b 2 ⋅ 2 = 3 4 a 6 b 4 ⋅ 3 6 b 4 = 3 4 + 6 a 6 b 4 + 4 = 3 10 a 6 b 8

Answered by Anonymous | 2024-06-10

To solve the first expression, we found that ( − 3 x y ) 3 ( − x 3 ) = 27 x 6 y 3 . For the second expression, we determined that ( − 9 b 2 a 3 ) 2 ( 3 3 b ) 2 = 729 b 6 a 6 . Both results were achieved by applying the rules of exponents and multiplication step-by-step.
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Answered by Lilith | 2024-10-02