Simplify 13𝑥 to the power of zero.
In order to answer this question, we need to recall one of our laws of exponents. 𝑎 to the power of zero is equal to one. This means that any letter or number raised to the power of zero equals one. In order to show why this works, let’s consider the number three raised to the power three, two, one, and zero.
We know that three to the power of three, or three cubed, is 27. Three squared is equal to nine. And three to the power of one is three. Each time our exponent decreases by one, we’re dividing the answer by three. As three divided by three is equal to one, three to the power of zero also equals one.
We could check this using any other base number. In our question, we are multiplying 13 by 𝑥 to the power of zero. Our order of operations tells us to evaluate the exponential term 𝑥 to the power of zero before multiplying. As we have just shown, anything to the power of zero is equal to one. We need to multiply 13 by one. As this equals 13, we can conclude that 13𝑥 to the power of zero is 13.
We can go one step further here and say that, for any constant 𝑏, 𝑏 multiplied by 𝑎 to the power of zero is equal to 𝑏.