**Let's see the following example:**

$a^4$

**Could you indicate what the exponent is?**

4 of course!

We can clearly see that the exponent is smaller and located at the top right corner of the base of the power.

The number of times that a) must be multiplied by itself is 4.

**We can say that:**

$a^4=a\times a\times a\times a$

In this example: a) must be multiplied by itself 4 times, as indicated by the exponent.

**Assignment**

Solve the following exercise:

$(4\times9\times11)^a$

**Solution**

We will use the formula

$(abc)^m=a^m\times b^m\times c^m$

We solve accordingly

$(4\times9\times11)^a=4^a\times9^a\times11^a=4^a9^a11^a$

**Answer**

$4^a9^a11^a$

**Prompt**

$\left(4^x\right)^y=$

**Solution**

We multiply the two powers together.

$4^{x\times y}=4^{xy}$

**Answer**

$4^{xy}$

$2^{-5}=\text{?}$

**Solution**

$2^{-5}=2^{0-5}=$

$\frac{2^0}{2^5}=$

$\frac{1}{2^5}=$

We solve the exercise in the fraction according to the power

$2^5=2\times2\times2\times2\times2=$

We solve the multiplications from left to right

$4\times2\times2\times2=$

$8\times2\times2=$

$16\times2=32$

**Answer**

$\frac{1}{32}$

**Assignment**

$4^{-1}=\text{?}$

**Solution**

$4^{-1}=\frac{4^0}{4^1}=$

$\frac{1}{4}$

**Answer**

$\frac{1}{4}$

The exponent of a base is the number that is found in the upper right part of the base and it is the number that represents or indicates how many times the base should be multiplied by itself.

**For example:**

$2^4=$

In this power, the base is $2$ and the exponent is $4$, therefore the exponent indicates that the two should be multiplied by itself $4$ times, that is:

$2^4=\text{ }2\times2\times2\times2$

When a power does not explicitly have an exponent, that is, it lacks an exponent, we must assume that it has an exponent $1$

**Examples:**

$a=a^1$

$3=3^1$

$7=7^1$

In this case, the base will be one, and for this type of power the following holds true:

$1^m=1$

This property tells me that the base one raised to any power will result in $1$, since one is always multiplied several times, or in this case, the number of times indicated by the exponent.

**Examples**

$1^3=1\times1\times1=1$

$1^5=1$

$1^8=1$