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**13. Exponents and Powers**

**Exponents and Powers**

An **exponent or power** is a mathematical representation that indicates the number of times that a number is multiplied by itself.

An **exponent or power** is a mathematical representation that indicates the number of times that a number is multiplied by itself.

If a number is multiplied by itself m times, then it can be written as: a x a x a x a x a...m times = am

Here, a is called the** base**, and m is called the **exponent, power or index.**

Numbers raised to the** power **of two are called **square numbers.**

**Square numbers **are also read as two-square, three-square, four-square, five-square, and so on.

Numbers raised to the power of three are called** cube numbers.**

**Cube numbers **are also read as two-cube, three-cube, four-cube, five-cube, and so on.

**Negative numbers** can also be** written using exponents.**

If an = b, where a and b are **integers** and n is a **natural number**, then an is called the** exponential form of b.**

The** factors** of a product can be expressed as the** powers **of the **prime factors** of 100.

This form of **expressing numbers** using **exponents** is called the** prime factor product form of exponents.**

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Even if we interchange the** order of the factors**, the value remains the same.

So a raised to the power of x multiplied by b raised to the power of y, is the same as b raised to the power of y multiplied by a raised to the power of x.

The value of an **exponential number** with a negative base raised to the power of an **even number is positive.**

If the base of two **exponential numbers** is the same, then the number with the **greater exponent** is greater than the number with the **smaller exponent.**

A number can be expressed as a **decimal number** between 1.0 and 10.0, including 1.0, multiplied by a power of 10. Such a form of a number is known as its **standard form.**

**Laws of Exponents**

When numbers with the same base are multiplied, the **power of the product.**

When numbers with the same base are multiplied, the power of the product is equal to the sum of the powers of the numbers.

More precisely if m and n are whole numbers then,

When numbers with the same base are divided, then the **power of the quotient is** equal to the difference between the powers of the dividend and the divisor. That is, if is a non-zero integer, and m and are whole numbers then, **a ^{m} Ã· a^{n} = a^{m-n}**

**The other laws of exponents are as follows:**

1) **a ^{m} Ã· a^{n} = a^{m-n} ** , where> are non - zero integers, and

2) **a ^{m} Ã· a^{n} = a^{m-n}** , where are non - zero integers, and

3) **a ^{m} Ã· a^{n} = a^{m-n} ** ,where> a is a non-zero integer, and m and n are whole numbers.

4) **a ^{0} = 1,** The value ,where> a is a non-zero integer.

5) ,where> a is a non - zero integer, and m and n are whole numbers.

211 videos|109 docs|45 tests

### NCERT Textbook - Exponents and Powers

- Doc | 16 pages
### NCERT Solutions(Part - 2) - Exponents and Powers

- Doc | 4 pages
### Introduction to Exponents

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### Understanding: Powers with the Same Exponent

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### Worksheet Question - Exponents and Powers

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### Writing Numbers as a Product of Powers of Prime Factors

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- Test: Exponents And Powers - 1
- Test | 20 ques | 10 min
- NCERT Solutions(Part - 1) - Exponents and Powers
- Doc | 6 pages