Exponents lecture 2

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.

If x is a positive real number and the exponents are rational numbers, Find: ((x^a)/(x^b))^(a^2+b^2-a b). ((x^b)/x^c)^(b^2+c^2-b c). ((x^c)/(x^(a)))^(c^2+a^2-c a)

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 : 2^(-5)-:2^2

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

Using the laws of exponents simplify and express each of the exponential form with positive exponent : 3^(-4)\ "x"\ 2^(-4)