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Powers for Kids - Math for Kids -  Basic Concepts

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The exponent of a number says how many times to use the number in a multiplication.

In words: 8 ² could be called "8 to the power 2" or "8 to the second power", or simply "8 squared"
Exponents are also called Powers or Indices.
Some more examples:

Example: 5³ = 5 × 5 × 5 = 125

In words: 5³ could be called "5 to the third power", "5 to the power 3" or simply "5 cubed"

Example: 2⁴ = 2 × 2 × 2 × 2 = 16

In words: 2⁴ could be called "2 to the fourth power" or "2 to the power 4" or simply "2 to the 4th"

Exponents make it easier to write and use many multiplications

Example: is easier to write and read than 9 × 9 × 9 × 9 × 9 × 9

You can multiply any number by itself as many times as you want using exponents.

Try here:

algebra/images/exponent-calc.js

So in general:

a n tells you to multiply a by itself,
so there are n of those a's:

Another Way of Writing It

Sometimes people use the ^ symbol (above the 6 on your keyboard), as it is easy to type.

Example: 2^4 is the same as 2⁴

Negative Exponents

Negative? What could be the opposite of multiplying? Dividing!

So we divide by the number each time, which is the same as multiplying by

We can continue on like this:

Example: 5⁻³ = 1 1 1 5 = 0.0085 × 5 ×

But it is often easier to do it this way:

5⁻³ could also be calculated like:

Negative? Flip the Positive!

That last example showed an easier way to handle negative exponents:

Calculate the positive exponent (an)

Then take the 1/aReciprocal (i.e. n)

More Examples:

What if the Exponent is 1, or 0?

It All Makes Sense

If you look at that table, you will see that positive, zero or negative exponents are really part of the same (fairly simple) pattern:

Example: Powers of 5

.. etc..

5²
5 × 5

25

5¹
5

5

5⁰
1

1

5⁻¹
1 5

0.2

5⁻²
1 1 5 5 ×

0.04

.. etc..

Be Careful About Grouping

To avoid confusion, use parentheses () in cases like this:

305, 1679, 306, 1680, 1077, 1681, 1078, 1079, 3863, 3864

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The exponent of a number says how many times to use the number in a multiplication. In words: 8 2 could be called "8 to the power 2" or "8 to the second power", or simply "8 squared" Exponents are also called Powers or Indices.

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Learn about the concept of exponents and how to evaluate powers, how to multiply & divide powers, and to raise powers to powers. Watch now!

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What is an Exponent? | An Intro to Exponents | Math with Mr. J

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https://www.alisonsmontessori.com/Exponents_Cloth_Chart_p/m625.htm?srsltid=AfmBOoqtr4VTMmA-_3GRUgsU_1wuV_1AFzisJ-XqXt8k9k2VE4_GGg0W