Exponents

Exponents are a mathematical operation used for numbers/variables multiplied an n amount of times. Exponents involve two numbers, the base b and the power or exponent n.

Basic exponents: Power of 0 and 1

Before diving into other exponents, the basics must be understood: powers of 0 and 1.

Starting off with the simpler exponent: 1. If we raise a number to the power of 1, we will have the same number. A power of 1 can be seen as the same thing as the number itself, or multiplying the number by 1.

For example, ${\displaystyle 2^{1}=2}$ because it is the same as ${\displaystyle 2*1=2}$. ${\displaystyle 5^{1}=5}$ which is the same as ${\displaystyle 5*1=5}$.

When we look at raising a number to the power of 0, it's a bit trickier. You might think that any number raised to the power of 0 will just be 0 if we use the prior method of multiplying the base by the power, but that is not the case. Any number raised to the power of 0 will be 1.

For example, ${\displaystyle 2^{0}=1}$ and ${\displaystyle 5^{0}=1}$.

The reasoning behind it is a lot more complex for pre-algebra, but just remember that any number with a power of 0 is 1.

Basic exponents: Squaring numbers

The most basic exponent is the square, which refers to a power of 2. Raising exponents to the power of 2 is the same as multiplying the base by itself once.

For example, ${\displaystyle 2^{2}=4}$ because ${\displaystyle 2*2=4}$; or ${\displaystyle 5^{2}=25}$ because ${\displaystyle 5*5=25}$.

Exponents refer to how many times a number is multiplied by itself. So if we have larger exponents like a power of 3 or 4, we would want to multiply our base value by the number of times of our power.

It is very important to know what our first 12 perfect squares are:

• ${\displaystyle 1^{2}=1}$
• ${\displaystyle 2^{2}=4}$
• ${\displaystyle 3^{2}=9}$
• ${\displaystyle 4^{2}=16}$
• ${\displaystyle 5^{2}=25}$
• ${\displaystyle 6^{2}=36}$
• ${\displaystyle 7^{2}=49}$
• ${\displaystyle 8^{2}=64}$
• ${\displaystyle 9^{2}=81}$
• ${\displaystyle 10^{2}=100}$
• ${\displaystyle 11^{2}=121}$
• ${\displaystyle 12^{2}=144}$

Larger exponents

Exponents greater than 2 follow the formula of ${\displaystyle n^{x}=n*n*n...}$ for x amount of times.

For example, ${\displaystyle 2^{3}=8}$ which is the same as ${\displaystyle 2*2*2=8}$. Similarly, ${\displaystyle 2^{4}=16}$, which is the same as ${\displaystyle 2*2*2*2=16}$.

Think about exponents as multiplying your base value by itself the number of times your power is. For ${\displaystyle 2^{3}}$, we multiply 2 by itself 3 times. For ${\displaystyle 2^{4}}$, we multiply 2 by itself 4 times.