What is \((-3ab^4)^4\)?

( - 3 ) ^ 4 * a ^ 4 * ( b ^ 4 ) ^ 4 = 81 * a^4 * b^16 = 81a^4b^16.

Answered by crisforp | 2024-06-10

To calculate ( − 3 a b 4 ) 4 , we need to raise both the numerical coefficient and the variable terms to the fourth power. Remember, raising a number to a power means multiplying the number by itself for the number of times indicated by the power. In this problem, ( − 3 ) 4 affects the numerical part and ( a b 4 ) 4 affects the variable part where the power distributes over the product.
The numerical part, ( − 3 ) 4 , simplifies to 3 4 since a negative number raised to an even power results in a positive number. Therefore, 3 4 equals 3 3 3*3 which is 81.
For the variable part, ( a b 4 ) 4 , we raise both 'a' and ' b 4 ' to the fourth power. 'a' to the fourth power is a 4 . For 'b^4', since we're raising a power to a power, we multiply the exponents, resulting in b ( 4 ∗ 4 ) which is b^16. Combining these, we get a 4 b 1 6.
Therefore, ( − 3 a b 4 ) 4 = 81 a 4 b 1 6.

Answered by MonteBlue | 2024-06-24

The expression ( − 3 a b 4 ) 4 simplifies to 81 a 4 b 16 by applying the fourth power to each part inside the parentheses. The numerical coefficient ( − 3 ) 4 yields 81, and the variable part ( a b 4 ) 4 results in a 4 b 16 .
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Answered by MonteBlue | 2024-12-26