It is known that a>0 and b<0. Compare the values of the following expressions to zero:
ab^2
i dont understand why i always get these wrong, i pluged in numbers that match with what it says and i solve:
1*-1^2=-1, 0 is greater than ab^2
but i got that wrong i dont understand why though
b^2 is always positive, so since a>0,
ab^2 > 0
If you are using 1, -1 * -1 = 1
1 * (-1^2) = 1 * 1 = 1
Oh, dear human, it seems like you have stumbled upon an interesting scenario. Let me help you with a dash of humor.
Now, in this problem, we have a delightful little equation: ab^2. You correctly identified that a is greater than zero (that's a positive number) and b is less than zero (a negative little fella).
Here comes the twist – when you square a negative number like b, it becomes positive! So, even though b is negative, b^2 will be positive. Now, when you multiply a positive number (a) with a positive number (b^2), the result will be positive as well.
Therefore, my friend, ab^2 will always be greater than zero! It's like trying to win a staring contest with a cat – you just can't beat the cuteness.
In order to compare the expression ab^2 to zero, we need to understand the properties of exponents and the signs involved.
Given that a > 0, we know that it is a positive number. Similarly, b < 0 means that b is a negative number.
Now let's simplify the expression ab^2 step by step:
First, we substitute the given values of a and b:
ab^2 = (a)(b^2)
Since a > 0, we have:
(a)(b^2) > 0 * (b^2) [Multiplying a positive number by any value less than zero gives a negative value]
Next, we consider the value of b. In this case, b is a negative number.
If we square a negative number, the result will always be positive. For example, (-1)^2 = 1, (-2)^2 = 4, and so on. So we can rewrite (b^2) as a positive number:
(a)(b^2) > 0 * positive_number
Since the product of a positive number and a positive number is positive, we have:
(a)(b^2) > 0
Hence, we can conclude that the expression ab^2 is always positive and greater than zero for the given conditions a > 0 and b < 0.
You mentioned that you obtained -1 as your result when you plugged in specific values (a = 1 and b = -1) into the expression. However, it seems like you might have made a mistake when calculating the exponent.
Remember that an exponent takes precedence over multiplication or addition. So, in the original expression ab^2, you should square b first and then multiply it by a.
Using a = 1 and b = -1, let's calculate the expression correctly this time:
ab^2 = 1 * (-1)^2 = 1 * 1 = 1
So, ab^2 is indeed positive and greater than zero when a > 0 and b < 0.