reduce to lowest terms
75a^2b
__________
25ab^2
Do these with like terms:
75/25
then
a^2/a
then b/b^2
To reduce the expression 75a^2b / 25ab^2 to lowest terms, we need to simplify each part of the expression individually.
First, let's simplify the numerical part 75/25. Dividing 75 by 25 gives us 3.
Next, let's simplify the variable part a^2/a. When dividing variable terms with the same base, we subtract their exponents. In this case, we have a^2 / a, which simplifies to a^(2-1) = a^1 = a.
Finally, let's simplify the variable part b/b^2. Again, when dividing variable terms with the same base, we subtract their exponents. Here, we have b / b^2, which simplifies to b^(1-2) = b^(-1). Since any number or variable to the power of -1 is equal to its reciprocal, b^(-1) is equal to 1/b.
Putting it all together, the expression reduces to:
3a / (1/b)
To simplify it further, we can multiply the numerator and denominator by b to get rid of the fraction in the denominator:
(3a * b) / 1
= 3ab
So, the reduced form of the expression 75a^2b / 25ab^2 is 3ab.