Answering this question is a matter of taking the reciprocal of a fraction, which means flipping it so that its numerator becomes the denominator and vice versa. We can simplify the expression:
First, before taking the absolute value of the expression,
which is just the positive “version” of the resulting value, you
need to carry out the expression within the absolute value signs.
The first term, 4–1⁄2, uses the properties
that any number or term raised to a negative power is equal to the
reciprocal of that base raised to the opposite power and that a
fractional power is equivalent to taking the root. Therefore, 4–1⁄2 =
This is a simple substitution problem. Plug in 3 for x and simplify. Noticing the fact that the least common multiple of 4 and 5 is 20 makes the simplification process easier:
A negative base raised to an odd power, like yz, is negative. When this is multiplied by a positive even number, the result is negative and even. –24 is the only negative even choice among the possibilities, so it must be the right answer.
This is a simple substitution question as long as you know logarithms and remember the rules for division by a fraction. After substituting 4 into the equation in place of x, the expression simplifies to