By what number (23)-3 should be multiplied so that the product becomes...
To find the number by which (23)-3 should be multiplied to become (69)-1, we can set up the equation:
x * (23)-3 = (69)-1
Simplifying the given expressions, we have:
(23)-3 = 23 * 23 * 23
(69)-1 = 1/69
Substituting these values back into the equation, we have:
x * (23 * 23 * 23) = 1/69
Solving for x:
x = (1/69) / (23 * 23 * 23)
Now, let's simplify the expression on the right-hand side:
x = 1/69 / (23 * 23 * 23)
Since dividing by a fraction is the same as multiplying by its reciprocal, we can rewrite the expression as:
x = 1/69 * (1 / (23 * 23 * 23))
Simplifying further:
x = 1 / (69 * 23 * 23 * 23)
Now, let's calculate the value of x:
x = 1 / (69 * 23 * 23 * 23)
x = 1 / (69 * 12167)
x = 1 / 838,323
x ≈ 0.000001192
Thus, the correct answer is option C) 529/3, which is approximately equal to 0.000001192.