## How to Divide Exponents

Read,3 minutes

So, in layman terms, **exponent **of a number is basically referred to as the **power **of that number. So, for example, we have often seen this phrase in mathematics “\(2\) to the power \(4\)”. So, this is nothing but \(2^4\). This generally means that \(2\) is **multiplied **by itself \(4\) times. So, the general expression could be written as \(2 \times 2 \times 2 \times 2\).

Exponents are basically used to **reduce **the length of an algebraic expression. We know how tedious would it be if we had to write “\(2\) to the power \(10\)” in the general form without the exponent. \(2^10\) is a very **simple **and **less tedious **way to write this.

Now, let’s consider the exponent case of \(2^4\). In this case, \(2\) is referred to as the "**base**," while \(4\) is referred to as the "**exponent**" or "**power**." In the term \(x^n\):

- \(n\) is the
**exponent**or power - \(x\) is called the
**base**

### Properties of Exponents

When dealing with exponents, it is **necessary **to apply the properties of exponents or the rules of exponents in order to solve the problem. These characteristics are also referred to as **major **exponents rules, which must be observed when solving exponent problems. The next section discusses the properties of exponents.

- The
**Product**Law states that \(a^m \times a^n \ = \ a^{m \ + \ n}\) - The Law of
**Quotients**states that \(\frac{a^m}{a^n} \ = \ a^{m \ - \ n}\) - The Law of the
**Zero**Exponent is as follows: \(a^0 \ = \ 1\) - The Law of the
**Negative**Exponent states that \(a^{-m} \ = \ \frac{1}{a^m}\) - The Law of the
**Power**of a**Power**is as follows: \((a^m)^n \ = \ a^{m \times n}\) - The Power of a
**Product**is defined as \((ab)^m \ = \ a^m \times b^m\) - The Power of a
**Quotient**is defined as \((\frac{a}{b})^m \ = \ \frac{a^m}{b^m}\)

### Division Properties of Exponents

Some **division **properties of exponents are:

- The Law of
**Quotients**states that \(\frac{a^m}{a^n} \ = \ a^{m \ - \ n}\) - The Power of a
**Quotient**is defined as \((\frac{a}{b})^m \ = \ \frac{a^m}{b^m}\)

### Exercises for Division Property of Exponents

**1) **\( \frac{22x^7}{2x^3} = \)

**2) **\( \frac{9^5}{9} = \)

**3) **\( \frac{6x^6}{2x^3} = \)

**4) **\( \frac{24x^{-7}}{3x^{-3}} = \)

**5) **\( \frac{18x^{-6}}{2x^{-2}} = \)

**6) **\( \frac{16x^6}{4x^3} = \)

**7) **\( \frac{2^6}{2} = \)

**8) **\( \frac{10x^{-8}}{2x^{-3}y^{2}} = \)

**9) **\( \frac{18x^{-7}}{3x^{-4}y^{3}} = \)

**10) **\( \frac{3^5}{3} = \)