Question Video: Finding the Numerical Value for an Algebraic Expression Using Laws of Exponents Mathematics

Video Transcript

What is the value of two to the 𝑥 plus seven power minus two to the 𝑥 plus four power divided by two to the 𝑥 power?

In order to find the value of this expression, we can use the fact that 𝑎 to the 𝑚 plus 𝑛 power is equal to 𝑎 to the 𝑚 power times 𝑎 to the 𝑛 power. And we can use this on two to the 𝑥 plus seven power and two to the 𝑥 plus four power.

So this would turn into two to the 𝑥 power times two to the seventh power minus two to the 𝑥 power times two to the fourth power. And this is all divided by two to the 𝑥 power. But let’s go ahead and rewrite the division of two to the 𝑥 power.

Now moving on, notice on the numerator we can take out a greatest common factor of two to the 𝑥 power. And the benefit of taking out this greatest common factor is it will cancel with the denominator of two to the 𝑥 power. So we would be left with two to the seventh power minus two to the fourth power.

So let’s evaluate each of these and then subtract. Two to the seventh power is equal to 128, and two to the fourth power is equal to 16. And 128 minus 16 is equal to 112. Therefore, this will be our final answer.