Without using a mathematical table or a calculator, evaluate:
(256/81)-¼ * ( 343)⅔
To evaluate this expression without a calculator, let's break it down step by step.
First, simplify (256/81):
256/81 = (64 * 4) / (9 * 9) = 64/9.
Next, evaluate (343)^(2/3):
343^(2/3) = (7^3)^(2/3) = 7^(2) = 49.
Now, substitute these values back into the original expression:
(64/9) - 1/4 * 49.
Now evaluate the subtraction:
64/9 - 49/4.
To subtract these fractions, you need a common denominator, which in this case is 36. So, rewrite the fractions with the common denominator:
(64/9) = (64/9) * (4/4) = 256/36,
(49/4) = (49/4) * (9/9) = 441/36.
Now do the subtraction:
256/36 - 441/36 = (256 - 441) / 36 = -185 / 36.
Therefore, the result of the expression is -185/36.