What is the value of ` y ^(x ) +(2x - 2y ) ` when x=2 and y=-3 ?

Options

A. `-10`
B. `1`
C. `7`
D. `19`

Answer

To find the value of the expression \( y^x + (2x - 2y) \) when \( x = 2 \) and \( y = -3 \), we will follow these steps:

### Step 1: Substitute the values of \( x \) and \( y \) into the expression.
Given:
- \( x = 2 \)
- \( y = -3 \)

The expression becomes:
\[ y^x + (2x - 2y) = (-3)^2 + (2(2) - 2(-3)) \]

### Step 2: Calculate \( y^x \).
Now, calculate \( (-3)^2 \):
\[ (-3)^2 = 9 \]

### Step 3: Calculate \( 2x - 2y \).
Next, calculate \( 2(2) - 2(-3) \):
\[ 2(2) = 4 \]
\[ -2(-3) = 6 \]
So,
\[ 2x - 2y = 4 + 6 = 10 \]

### Step 4: Combine the results.
Now, we combine the results from Step 2 and Step 3:
\[ y^x + (2x - 2y) = 9 + 10 = 19 \]

### Final Answer:
Thus, the value of the expression when \( x = 2 \) and \( y = -3 \) is:
\[ \boxed{19} \]

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