Laws of Indices

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Laws of Indices

‘Indices’ is the plural form of index. And, index means power of any number or variable term, which is called a base. Power or index is also known as an exponent.

Coefficient, base and index

There are certain rules which are used to solve the problems of indices. These rules are called the laws of indices. Some laws of indices are as follows:

Laws of indices


Problems involving laws of indices 

Example 1: Find the value of: 〖27〗^(4/3)

Example 2: Find the value of: 〖(2401)〗^(- 1/4)

Example 3: Find the value of: [√(3&64) ÷ (1/125)^((-1)/3) ]^2

Example 4: Find the value of: (81/16)^((-3)/4) × [(25/9)^((-3)/2) ÷ (5/2)^(-3) ]

Example 5: Find the value of: (x^a/x^(-b) )^(a-b) × (x^b/x^(-c) )^(b-c) × (x^c/x^(-a) )^(c-a)


Example 6: Simplify: (x^a÷x^b )^(a^2+ab+b^2 )× (x^b÷x^c )^(b^2+bc+c^2 )× (x^c÷x^a )^(c^2+ca+a^2 )

 Example 7: Simplify: √(ab&x^a/x^b ) × √(bc&x^b/x^c ) × √(ca&x^c/x^a )


Example 8: Simplify: 1/(1+ x^(a-b)+ x^(a-c) )+ 1/(1+ x^(b-c)+x^(b-a) )+ 1/(1+ x^(c-a)+ x^(c-b) )


Example 9: Simplify: (x^(a+b)/x^c )^(a-b) × (x^(b+c)/x^a )^(b-c) × (x^(c+a)/x^b )^(c-a)


Example 10: Find the value of: (2^(n+1) × 2^((n-1)(n+1)))/(2^(n(n-1)) × 4^(n+1) )

 

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