(4 − 2x)−2
x=-2
y=4
z=-3
how do you solve this? i have solved it and gotten 6 for my answer many times and it says it's wrong.
other equations are (y − z)−3 and (x − 5y)0. i cant get them right
First, please proofread your post. It appears you are trying to solve
4-2x = -2
y - z = -3
x - 5y = 0
But that does not appear to fit the other data. How is the question actually presented?
Write your 3 equations exactly, and then we can make some progress.
147
To solve the expression (4 − 2x)−2, you need to follow the order of operations, which is also known as PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).
Substituting the given values of x, y, and z, we have:
x = -2,
y = 4,
z = -3.
Let's solve the expression step by step:
Step 1: Substitute the value of x into the expression: (4 − 2(-2))−2 becomes (4 + 4)−2.
Step 2: Simplify the expression inside the parentheses: (8)−2.
Step 3: Evaluate the exponent: This means we need to raise 8 to the power of -2, which is equivalent to taking the reciprocal of 8 squared. In other words, it becomes 1/8², which simplifies to 1/64. So, the expression simplifies to:
1/64.
Therefore, the correct answer for the expression (4 − 2x)−2, given x = -2, is 1/64.
Moving on to the other equations:
(y − z)−3:
Substituting the values of y and z, we have y = 4 and z = -3.
The expression becomes (4 - (-3)) ^ (-3). Simplifying it further, we get (4 + 3) ^ (-3).
The exponent -3 indicates that the expression needs to be raised to the power of -3. When we raise (4 + 3) to the power of -3, we get 1/(4 + 3)^3, which simplifies to 1/7^3. Evaluating further, 1/7^3 equals 1/343.
Therefore, the correct answer is 1/343.
(x − 5y)0:
In this equation, the exponent is 0, which means anything raised to the power of 0 is always equal to 1.
Substituting the values of x and y, we have x = -2 and y = 4.
So, the expression becomes (-2 - 5 * 4)^0.
Simplifying further, we have (-2 - 20)^0.
Since the expression has an exponent of 0, it evaluates to 1.
Therefore, the correct answer is 1.
To recap:
- The correct answer for (4 - 2x)^(-2) with x = -2 is 1/64.
- The correct answer for (y - z)^(-3) with y = 4 and z = -3 is 1/343.
- The correct answer for (x - 5y)^0 with x = -2 and y = 4 is 1.