(4³)-²×(2³)⁴×(8/15)-²
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Answer:
225/64
Step-by-step explanation:
Simplify the following:
(2^3)^4/((4^3)^2 (8/15)^2)
Multiply exponents. (4^3)^2 = 4^(3×2):
(2^3)^4/(4^(3×2) (8/15)^2)
Multiply exponents. (2^3)^4 = 2^(3×4):
2^(3×4)/(4^(3×2) (8/15)^2)
3×2 = 6:
2^(3×4)/(4^6 (8/15)^2)
3×4 = 12:
2^12/(4^6 (8/15)^2)
(8/15)^2 = 8^2/15^2:
2^12/(4^6×8^2/15^2)
8^2 = 64:
2^12/(4^6×64/15^2)
| 1 | 5
× | 1 | 5
| 7 | 5
1 | 5 | 0
2 | 2 | 5:
2^12/(4^6×64/225)
4^6 = (4^3)^2 = (4×4^2)^2:
2^12/(((4×4^2)^2 64)/225)
4^2 = 16:
2^12/(((4×16)^2 64)/225)
4×16 = 64:
2^12/((64^2×64)/225)
| | 6 | 4
× | | 6 | 4
| 2 | 5 | 6
3 | 8 | 4 | 0
4 | 0 | 9 | 6:
2^12/((4096×64)/225)
2^12 = (2^6)^2 = ((2^3)^2)^2 = ((2×2^2)^2)^2:
((2×2^2)^2)^2/((4096×64)/225)
2^2 = 4:
((2×4)^2)^2/((4096×64)/225)
2×4 = 8:
(8^2)^2/((4096×64)/225)
8^2 = 64:
64^2/((4096×64)/225)
| | 6 | 4
× | | 6 | 4
| 2 | 5 | 6
3 | 8 | 4 | 0
4 | 0 | 9 | 6:
4096/(4096×64/225)
4096/(4096×64/225) = 4096/4096×1/(64/225) = 1/(64/225):
1/(64/225)
Multiply the numerator of 1/(64/225) by the reciprocal of the denominator. 1/(64/225) = (1×225)/64:
Answer: |
| 225/64