SOLUTION: Simplify (32/128)^¾ ÷ (1/64)^-0.5

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Question 1198058: Simplify (32/128)^¾ ÷ (1/64)^-0.5
Found 3 solutions by ankor@dixie-net.com, MathTherapy, greenestamps:
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Simplify (32/128)^¾ ÷ (1/64)^-0.5
We can reduce the the 1st fraction to:
%281%2F4%29%5E%283%2F4%29
the 2nd fraction, the reciprocal gets rid of the negative
it becomes times (*) %281%2F64%29%5E%281%2F2%29 which is sqrt%281%2F64%29 which is 1%2F8
we have
%281%2F4%29%5E%283%2F4%29+%2A++%281%2F8%29

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

Simplify (32/128)^¾ ÷ (1/64)^-0.5
%28%2832%2F128%29%5E%283%2F4%29%29%2F%281%2F64%29%5E%28-+0.5%29

%28%281%2F4%29%5E%283%2F4%29%29%2F%281%2F64%29%5E%28-+1%2F2%29 ------- Reducing the fractional-base in the numerator and changing - 0.5 to -+1%2F2 in the denominator

%28%281%2F4%29%5E%283%2F4%29%29%2Fmatrix%282%2C1%2C+%22+%22%2C+%2864%29%5E%281%2F2%29%29 ----- Appying the law, matrix%281%2C3%2C+a%5E%28-+b%29%2C+%22=%22%2C+%281%2Fa%29%5Eb%29 in denominator

%28%282%5E%28-+2%29%29%5E%283%2F4%29%29%2F%282%5E6%29%5E%281%2F2%29%29 ------ Converting numerator's and denominator's bases to base 2

matrix%282%2C1%2C+%22+%22%2C+%282%5E%28-+3%2F2%29%2F%282%5E3%29%29%29 ---- Applying matrix%281%2C3%2C+%28a%5Eb%29%5Ec%2C+%22=%22%2C+a%5E%28bc%29%29

 ----- Applying matrix%281%2C3%2C+a%5Eb%2Fa%5Ec%2C+%22=%22%2C+a%5E%28b+-+c%29%29

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


To make the work easier to follow, simplify each of the two exponential expressions before performing the division.



%281%2F64%29%5E-0.5=64%5E0.5=8=2%5E3

Now perform the division.

%282%5E%28-3%2F2%29%29%2F%282%5E3%29=2%5E%28%28-3%2F2%29-3%29=2%5E%28-9%2F2%29

ANSWER (one of many possible forms): 2%5E%28-9%2F2%29 or 2%5E%28-4.5%29