This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
1 solution
The first equation is only true when the base of the power is 1 or 0. 1 to any power is always equal to 1 and 0 to any power (excluding 0) is also equal to 0.
However when we generalize the equation that the base and exponent can be any (real) number; a^p = a^q it is only true if p and q are the same.
Thus giving us the implication: IF a^p = a^q THAN p = q (in symbols: a^p = a^q => p = q)
We use a truth table to determine when an implication is true or false. As you can see, an implication is only false when the second statement is false and the first statement is true.
Since 1^2 is indeed equal to 1^3, the first statement is true. But since 2 is not equal to 3 the second statement is false, making the whole statement false.