Exponents lecture 1

Seven different lecturers are to deliver lectures in seven perday. A, B and C are three oftne lectures. The number of ways in which a routine for theday canr be made such that A delivers his lecture before B and B before C, is

The sum of the exponents of the prime factors in the prime factorisation of 196, is (a) 1 (b) 2 (c) 4 (d) 6

Write the sum of the exponents of prime factors in the prime factorization of 98.

The volume of one mole of ideal gas with adiabatic exponent is varied according to law V = 1/T . Find amount of heat obtained by gas in this process if gas temperature is increased by 100 K.

If x is a positive real number and the exponents are rational numbers, show that: ((x^a)/(x^b))^(a+b-c)\ ((x^b)/(x^c))^(b+c-a)((x^c)/(x^a))^(c+a-b)=1

Using the laws of exponents simplify and express each of the exponential form with positive exponent : (1/(2^3))^2

Expressed with positive exponents only , (ab^(-1))/(a^(-1) - b^(-1)) is equivalent to

Using the laws of exponents simplify and express each of the exponential form with positive exponent : 2^(-5)-:2^2

Using the laws of exponents simplify and express each of the exponential form with positive exponent : (-4)^4x\ (-4)^(-10)