4. what is the value of 2x^-2y^-2 for x=3 and y=-2?
1/18
72
2(-6)^-4
1/648
5.what is the value of 1/2-2x-3y5 for x=2 and 7=-4
16
-4
-1/32
-16
huh. Just plug in the numbers. I'll do the first one...
2x^-2y^-2 for x=3 and y=-2
= 2 * 3^-2 * (-2)^-2
= 2 * 1/3^2 * 1/(-2)^2
= 2 * 1/9 * 1/4
= 1/18
These aren't as hard as they look, as long as you are careful with each step.
so, what do you get for the other one?
To calculate the value of an expression with variables, you need to substitute the given values for the variables and simplify the expression using the exponent rules.
4. First, let's substitute the given values for x and y in the expression 2x^-2y^-2:
x = 3, y = -2
2(3)^-2(-2)^-2
To simplify exponents, we use the rule that says: when a negative exponent is in the denominator, it can be moved to the numerator and made positive. Therefore, (-a)^-b would become 1/(-a)^b.
2/((3^2)(-2)^2)
Then, we calculate the values of the exponents:
2/(9)(4)
Now, we simplify the expression:
2/36 = 1/18
Therefore, the value of 2x^-2y^-2, when x=3 and y=-2, is 1/18.
5. Now, let's substitute the given values for x and y in the expression 1/2-2x-3y5:
x = 2, y = -4
1/2-2(2)-3(-4)^5
First, let's calculate the exponent:
(-4)^5 = -1024
Now, substituting the values:
1/2-2(2)-3(-1024)
Simplifying the multiplication:
1/2-4-3(-1024)
Multiplying -3 by -1024:
1/2-4+3072
Simplifying further:
1/2+3068 = 3069/2
Therefore, the value of 1/2-2x-3y5, when x=2 and y=-4, is 3069/2.