1.

Evaluate 8x2y−2 for x = –1 and y = 2.

32

2

8(−2)0

1 answer

To evaluate the expression \( 8x^2y^{-2} \) for \( x = -1 \) and \( y = 2 \), follow these steps:

1. **Substitute the given values of x and y into the expression:**

\[ 8(-1)^2 \cdot (2)^{-2} \]

2. **Evaluate the square of -1:**

\[ (-1)^2 = 1 \]

So the expression now simplifies to:

\[ 8 \cdot 1 \cdot (2)^{-2} \]

3. **Evaluate \( (2)^{-2} \):**

Recall that \( a^{-n} = \frac{1}{a^n} \), so:

\[ (2)^{-2} = \frac{1}{2^2} = \frac{1}{4} \]

4. **Multiply the simplified components together:**

\[ 8 \cdot 1 \cdot \frac{1}{4} = 8 \cdot \frac{1}{4} = 2 \]

So, the value of the expression when \( x = -1 \) and \( y = 2 \) is \( 2 \).