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Alfredo Curry
Mathematics
11 December, 15:23
Evaluate 1 / 2^-2x^-3y^5 for x=2 and y=-4
+4
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1
)
Brenda Schneider
11 December, 15:46
0
-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
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