WHAT IS 3 TO THE FOURTH POWER

     

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

Bạn đang xem: What is 3 to the fourth power

*

In 82 the "2" says to lớn use 8 twice in a multiplication,so 82 = 8 × 8 = 64

In words: 82 could be called "8 to lớn the nguồn 2" or "8 to lớn 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 lớn the third power", "5 to lớn 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 lớn the power 4" or simply "2 to the 4th"

So in general:

an tells you lớn 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 khổng lồ type.

Xem thêm: Bộ Đề Thi Học Kì 2 Môn Sinh Học Lớp 8 Năm 2020, 11 Đề Thi Học Kì 2 Môn Sinh Lớp 8 Năm 2020


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 1number


Negative? Flip the Positive!

*

That last example showed an easier way khổng lồ handle negative exponents:

Calculate the positive exponent (an)

More Examples:


Negative Exponent Reciprocal ofPositive Exponent Answer
4-2 = 1 / 42 = 1/16 = 0.0625
10-3 = 1 / 103 = 1/1,000 = 0.001
(-2)-3 = 1 / (-2)3 = 1/(-8) = -0.125

What if the Exponent is 1, or 0?

1 If the exponent is 1, then you just have the number itself (example 91 = 9)
0 If the exponent is 0, then you get 1 (example 90 = 1)
But what about 00 ? It could be either 1 or 0, và so people say it is "indeterminate".

It All Makes Sense

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


Example: Powers of 5
.. Etc..

Xem thêm: Một Pin Có Số Ghi Trên Vỏ Là 1 5V, A)Trên Vỏ Của Một Pin Còn Mới Có Ghi 1,5V

*
52 5 × 5 25
51 5 5
50 1 1
5-1 15 0.2
5-2 15 × 15 0.04
.. Etc..