Here we are going to see, "Exponents and Scientific notation rules".

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

for example 5³ = 5 x 5 x 5

In words 5³ could be called as 5 to the power 3 or 5 cube.

10² is called as 10 to the power 2 or simply called as 10 square. | |

10 | |

If we have 1/2 in the power, we can simply write the base inside the radical or square root. If we have 1/3 in the power,we can simply write the base inside the cube root |

If the power goes from one side of equal sign to the other side,it will flip.that is x = 4² |

The other names of exponent are index and power.

**Rule 1 :**

Whenever we have to simplify two or more the terms which are multiplying with the same base,then we have to put the same base and add the powers.

**Rule 2 :**

Whenever we have two terms, which are diving with the same base,we have to put only one base and we have to subtract the powers.

**Rule 3 :**

**Rule 4 :**

**Anything to the power zero is 1.**

**Rule 5 :**

If we have same power for 2 or more terms which are multiplying or dividing,we have to apply the powers for every terms.Note:This rule is not applicable when two are more terms which are adding and subtracting.For example (x + y) ^m = (x^m + y^m) is not correct

Other things:

Point 1:

If we don't have any number in the power then we have to consider that there is 1

Point 2:

In case we have negative power for any fraction or any integer and if we want to make it as positive,we can write the power as positive and we should write its reciprocal only.

A number is written is scientific notation when it is expressed in the form

To convert the given number into scientific notation, first we have identify where the decimal point and non zero digit come.

There are two cases in it.

**Case 1 : **

To move the decimal point to the left, we have to count number of digits as explained in the example given below.

According to the example given above, we have to move the decimal point 3 digits to the left and exponent of 10 should be 3 (positive integer)

When we do so, we get the scientific notation of the given number.

Hence, 2301.8 = 2.3018 x 10³

**Case 2 : **

To move the decimal point to the right, we have to count number of digits as explained in the example given below.

According to the example given above, we have to move the decimal point 5 digits to the right and exponent of 10 should be -5 (negative integer)

When we do so, we get the scientific notation of the given number.

Hence, 0.000023 = 2.3 x 10⁻⁵

Important Note:

If we don't find decimal point at anywhere of the given number, we have to assume that there is decimal point at the end of the number.

For example, 2300000 -------------> 2300000.

Here, the non zero digit comes first and decimal point comes next. So we have to apply case 1 to convert this number into scientific notation.

- Scientific notations
- Exponents and powers
- Example problems on exponents
- Sample problems on scientific notation
- Negative exponent rules
- Decimals

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