Evaluate
1/2^-2 x^-3 y^5
for x = 2 and y = –4
To evaluate the expression, we substitute the given values of x and y into the expression and simplify according to the rules of exponents.
The expression is: 1/2^-2 * x^-3 * y^5
We are given x = 2 and y = -4, so we substitute these values into the expression:
1/2^-2 * 2^-3 * (-4)^5
Let's simplify step by step. First, we simplify the negative exponents:
1/(1/2^2) * 1/(2^3) * (-4)^5
Next, we simplify the exponents with multiplication:
1/(1/4) * 1/8 * (-4)^5
We can simplify the first term by multiplying 1/(1/4):
4 * 1/8 * (-4)^5
The next step is to simplify the multiplication of the two fractions:
4/8 * (-4)^5
Now, we simplify the fraction 4/8, which is equal to 1/2:
1/2 * (-4)^5
Finally, we calculate the value of (-4)^5:
1/2 * (-1024)
Multiplying 1/2 by -1024 gives us:
-512
Therefore, the expression evaluates to -512 when x = 2 and y = -4.