One (1) Exponent Rule — Definition & Examples

Raising Numbers to the Power of One

If you raise any number to the power of $1,$ the result will be that number! This is one of the most simple exponent rules.

Let $x$ represent any number. Then:

For example:

$$\begin{align} 6^1&=6\\ (32x)^1&=32x\\ (x+y+z)^1&=x+y+z \end{align}$$

Notice that this rule isn't just limited to numbers. For instance, we can raise a variable to the first power. Both the second and third examples involve variables.

When we think of an exponent, say $a^b$, we can think of it as: $$a^b= \underbrace{a \cdot a \cdots a}_{b\text{ times}}$$

So, let's say $b=1$. Then $a^1 = a$, since there is only $1$ (one) $a$ in the right side of the equation above. Therefore, $a^1 = a$ for any real number $a$. This is one of the most important (and perhaps easiest to remember) exponent rules!

What about examples? Well, we could have $a$ be a positive integer:

$$4^1 = 4$$

The variable $a$ could also be a negative integer:

$$(-7)^1 = -7$$

Notice we keep the negative sign. It could also be a rational number, among other things:

$$\left(\frac{2577}{33}\right)^1 = \frac{2577}{33}$$

(Video) Powers of $0$ and $1$

by HEGARTYMATHS

Here's a video by HEGARTYMATHS going over some basic exponent rules. He goes over the product of powers, raising a number to $0$, and raising a number to $1$.

$\large{\text{Summary}}$

Anything raised to the power of $1$ is itself. For example, $2^1=2$. This is a pretty simple rule to understand because $a^1$ means $a$ just like how $a^2=a\cdot{a}$.

Let's look at an example. Suppose we want to simplify: $$7^1$$ Well, it's being raised to the power of $1$, so it'll just equal its base: $7$. Thus $$7^1=7$$