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

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, $2^{0}=1$ and $5^{0}=1$.

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, $2^{2}=4$ because $2*2=4$; or $5^{2}=25$ because $5*5=25$.

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:

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

Exercises

What are the squares?

1

10^2 is _.

_ =

2

3^2 is _.

_ =

3

8^2 is _.

_ =

4

4^2 is _.

_ =

5

7^2 is _.

_ =

Knowing our squares comes in handy when it comes to factoring and a method called completing the square.

Larger exponents

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

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

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

Exercises

What is the answer?

1

5^3 is _.

_ =

2

4^4 is _.

_ =

3

10^3 is _.

_ =

4

3^5 is _.

_ =

5

8^4 is _.

_ =

For more: Return to Pre-Algebra