Simplify : ( a + B )^(-1) . ( A^(-1) + B^(-1) ) - Mathematics

Simplify :
`( a + b )^(-1) . ( a^(-1) + b^(-1) )`

Sum

`( a + b )^(-1) . ( a^(-1) + b^(-1) )`

= `1/( a + b ) xx ( 1/a + 1/b )`

= `1/( a + b ) xx ([ b + a ]/[ ab ] )`

= `1/( a + b ) xx ( a + b )/(ab)`

= `1/(ab)`

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Laws of Exponents

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Chapter 7: Indices (Exponents) - Exercise 7 (A) [Page 98]

Chapter 7 Indices (Exponents)
Exercise 7 (A) | Q 2.2 | Page 98

Simplify :
`( 3x^2 )^(-3) xx ( x^9 )^(2/3)`

Evaluate:

`(27/8)^(2/3) - (1/4)^-2 + 5^0`

Simplify the following and express with positive index :
`(32)^(-2/5) ÷ (125)^(-2/3)`

If 1960 = 2^a. 5^b. 7^c, calculate the value of 2^-a. 7^b. 5^-c.

Simplify:

`[ 3 xx 27^( n + 1 ) + 9 xx 3^(3n - 1 )]/[ 8 xx 3^(3n) - 5 xx 27^n ]`

Simplify :
`( x^a/x^b)^( a^2 + ab + b^2 ) xx (x^b/x^c)^(b^2 + bc + c^2) xx (x^c/x^a)^( c^2 + ca + a^2 )`

If a = x^{m + n}. y^l; b = x^n + l. y^m and c = x^{l + m}. yⁿ,

Prove that : a^{m - n}. b^n - l. c^{l - m} = 1

Find the value of 10⁻³.

Find the value of (2³)².

Find the value of 4⁶ × 4⁻⁴.