4a³b×(3ab)–²
4 a³ b ( 3 a b )–² =
4 a³ b / ( 3 a b )² =
4 a³ b / ( 9 a² b² ) =
4 a² • a • b / ( 9 a² • b • b ) =
( a² • b ) • 4 a / ( a² • b • 9 b ) =
4 a / 9 b
4a/9b
The simplified form of the expression is 4a/9b.
To simplify the expression 4a³b × (3ab)–², we need to follow the order of operations, which is parentheses first, then exponents, and finally multiplication.
First, let's deal with the parentheses. In this case, we have (3ab)–². To simplify this, we can rewrite it as 1 / (3ab)². This is because raising a term to the power of -2 is the same as taking its reciprocal and squaring it.
Next, we can square the denominator by multiplying each term within the parentheses by itself.
(3ab)² = 3ab * 3ab = 9a²b².
So now, we have 4a³b × 1 / (9a²b²).
Next, we can simplify by canceling out common factors from the numerator and the denominator. We see that we can cancel out one factor of 'a' from a³ in the numerator and a² in the denominator, and one factor of 'b' from b in the numerator and b² in the denominator.
After canceling out the common factors, we are left with:
4a³b × 1 / (9 * 1) = 4a³b / 9.
Therefore, the simplified expression is 4a³b / 9.