For the next three problems, evaluate each expression if x = −2, y = 4, and z = −3.
(4 − 2x)−2
(y − z)−3
(x − 5y)0
(4-2(-2))-2 = (4-(-4)) = 4+4) = 8
(4-(-3))-3 = (4+3)-3 = 4+3-3 = 4
(-2-5(4))0 = 0
(anything times 0 = 0)
To solve these problems, you need to substitute the given values of x, y, and z into the expressions and simplify them.
Let's start with the first expression: (4 - 2x)^-2
Step 1: Substitute the values of x into the expression:
(4 - 2(-2))^(-2)
(4 + 4)^(-2)
8^(-2)
Step 2: Evaluate the expression:
8^(-2) = 1/8^2 = 1/64
So, when x = -2, the value of the expression (4 - 2x)^-2 is 1/64.
Next, let's move on to the second expression: (y - z)^-3
Step 1: Substitute the values of y and z into the expression:
(4 - (-3))^(-3)
(4 + 3)^(-3)
7^(-3)
Step 2: Evaluate the expression:
7^(-3) = 1/7^3 = 1/343
Therefore, when y = 4 and z = -3, the value of the expression (y - z)^-3 is 1/343.
Lastly, let's examine the third expression: (x - 5y)^0
Step 1: Substitute the values of x and y into the expression:
(-2 - 5(4))^0
(-2 - 20)^0
(-22)^0
Step 2: Evaluate the expression:
Anything raised to the power of 0 is equal to 1.
Therefore, when x = -2 and y = 4, the value of the expression (x - 5y)^0 is 1.