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

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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,   because it is the same as  .   which is the same as  .

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,   and  .

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

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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,   because  ; or   because  .

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:

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Exercises

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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

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Exponents greater than 2 follow the formula of   for x amount of times.

For example,   which is the same as  . Similarly,  , which is the same as  .

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

Exercises

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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