Question Video: Simplifying Algebraic Expressions Using the Laws of Exponents Mathematics • 10th Grade

Given 5^𝑥 = 2, determine the value of 25^𝑥.

01:51

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.