Consider how the expression was simplified in Part A.
A
Less than 1
B
See solution.
Practice makes perfect
We want to determine whether the expression ( 14^(-3))^(-2) is greater than 1, equal to 1, or less than 1. To evaluate the expression, we will use the Negative Exponent Property, which states that a^(- n) = 1a^n, assuming that a ≠0.
We can see that in the numerator we have 1 and in the denominator we have 4^6, which is greater than 1. This means that the result 14^6, which is equivalent to the expression ( 14^(-3))^(-2), is less than one.
In Part A we found that the value of the given expression is less than 1. Now we want to show how we can change one sign to make the value greater than 1. To do so, recall that in Part A we first used the Negative Exponent Property and simplified the given expression to (4^3)^(-2).
( 1/4^(-3))^(-2) = (4^3)^(-2)
Now, if the exponent outside the parentheses was not negative, we would have (4^3)^2, which would result in 4^6 and this number is greater than 1. Therefore, we can change the exponent -2 to 2 in ( 14^(-3))^(-2) to make the value of this expression greater than 1.
