The number 34613000 when expressed in exponential form is equal to

1. 3461.3 x 10³
2. 3.4613 x 10⁷
3. 0.34613 x 10⁹
4. 34.613 x 10⁵

Which is larger ?

(i) 2³ or 3²

(ii) 2⁵ or 5²

(iii) 3⁷ or 7³.

State True or False :

(i) For any non-zero number a, we have (a^m)ⁿ = a^m+n.

(ii) If a and b are non-zero numbers, then $\Big\lbrace\Big(\dfrac{a}{b}\Big)^m\Big\rbrace^n = \Big(\dfrac{b}{a}\Big)^{-mn}$

(iii) For a non-zero number x; (x^m x xⁿ) is equal to x to the power (m + n).

(iv) If a number p is multiplied n times, then the resulting number is pⁿ.

(v) In an exponential notation xⁿ; n is called the index.

A computer purchased for ₹72900 loses two-third of its value every year. Its value is evaluated at the end of every year.

(1) Which of the following expressions gives the value of the computer (in ₹) after n years?

1. $\dfrac{72900}{\Big(\dfrac{2}{3}\Big)^{n}}$

2. $\dfrac{2^{n} \times 27900}{3^{n}}$

3. $\dfrac{72900}{3^{n}}$

4. $\dfrac{72900}{2^{n} \times 3^{n}}$

(2) Find the value of the computer after 3 years.

1. ₹8100
2. ₹2430
3. ₹5600
4. ₹2700

(3) In how many years will the value of the computer be less than ₹200 ?

1. 6 years
2. 7 years
3. 8 years
4. 10 years

(4) By how much will the value of the computer reduce in 4 years ?

1. ₹24300
2. ₹1800
3. ₹8100
4. ₹72000