Evaluate 1 / 2^-2x^-3y^5 for x=2 and y=-4

-512

Step-by-step explanation:

Evaluate y^5 / (x^3/2^2) where x = 2 and y = - 4:

(y^5) / (2^ (-2) x^3) = (-4) ^5/2^ (-2) * 1/2^3

2^3 = 2*2^2:

(-4) ^5/2^ (-2) 1 / (2*2^2)

2^2 = 4:

(-4) ^5 / ((2*4) / 2^2)

2*4 = 8:

(-4) ^5 / (8/2^2)

2^ (-2) = 1/4:

((-4) ^5/8) / (1/4)

(-4) ^5 = (-1) ^5*4^5 = - 4^5:

((-4^5) / 8) / (1/4)

4^5 = 4*4^4 = 4 (4^2) ^2:

((-4 (4^2) ^2) / 8) / (1/4)

4^2 = 16:

((-4*16^2) / 8) / (1/4)

| 1 | 6

* | 1 | 6

| 9 | 6

1 | 6 | 0

2 | 5 | 6:

((-4*256) / 8) / (1/4)

4*256 = 1024:

((-1024) / 8) / (1/4)

Multiply the numerator by the reciprocal of the denominator, ((-1024) / 8) / (1/4) = (-1024) / 8*4:

(-1024*4) / 8

(-1024) / 8 = (8 (-128)) / 8 = - 128:

-128*4

-128*4 = - 512:

Answer: - 512