# Surd and Indices

**Vedic Maths trick to find which is greater value.**

### Property of Indices:

**a ^{m} * a^{n} = a^{m + n}**

**a ^{m} / a^{n} = a^{m - n}**

**( a ^{m} ) ^{n} = a^{m * n}**

**( ab ) ^{n} = a^{n} * b^{n}**

**( a / b ) ^{n} = a^{n} / b^{n}**

**( a ) ^{-n} = 1 / a^{n}**

**( a ) ^{1/n} = n√ a**

**( a ) ^{0} = 1**

### Property of Surd:

**n√ a = ( a ) ^{1/n}**

**n√ ab = ( a ) ^{1/n} * ( b )^{1/n}**

**n√ a/b = n√ a / n√ b**

**[ n√ a ] ^{n} = a **

**m√ n√ a = mn√ a **

**[ n√ a ] ^{m} =( a )^{m/n} **

##### Let's take 2 values **2√40** and **7√90**

#####
Find which is greater :

**= 40**^{1⁄2} and 90^{1⁄7}

Now we will find the LCM of the denominator of the power value :

LCM = 14

**= 40**^{7⁄14} and 90^{2⁄14}

**= 163840000000**^{1⁄14} and 8100^{1⁄14}

So, the greatest value is : 163840000000

^{1⁄2}and 90

^{1⁄7}

^{7⁄14}and 90

^{2⁄14}

^{1⁄14}and 8100

^{1⁄14}