Video Transcript
Given five to the 𝑥 power equals
two, determine the value of 25 to the 𝑥 power.
We have the equation five to the 𝑥
power equals two and the expression 25 to the 𝑥 power. We want to know what the value of
that expression is. At first glance, we notice that
five and 25 are not the same base. And that makes it difficult to do
any kind of simplification. But when we think about that 25 in
relation to five, we could say that 25 equals five squared. In our expression, in place of 25,
we can write five squared so that we have five squared to the 𝑥 power. Which reminds us that 𝑥 to the 𝑎
power to the 𝑏 power equals 𝑥 to the 𝑎 times 𝑏 power, which would be five to the
two times 𝑥 power.
But at this point, we still may be
puzzled because we only know what five to the 𝑥 power is; we don’t know what five
to the two 𝑥 power is. However, we can do some
regrouping. We know that five to the two 𝑥
power will also be equal to five to the 𝑥 power squared. What we’re saying is, five squared
to the 𝑥 power will have the same value as five to the 𝑥 power squared. This is true because they’re both
equal to five to the two 𝑥 power.
At this point, we know what five to
the 𝑥 power is equal to. Since five to the 𝑥 power equals
two, we can calculate five to the 𝑥 power squared as two squared, which equals
four. Given that five to the 𝑥 power
equals two, the value of 25 to the 𝑥 power is four.
