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

Assertion: $\dfrac{x^{4}}{y^{3}}$ can also be written as $\dfrac{x+x+x+x}{y+y+y}$.

Reason: In x^m, x is called the base and m is called the exponent.

1. Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
2. Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).
3. Assertion (A) is true but Reason (R) is false.
4. Assertion (A) is false but Reason (R) is true.

Assertion: x^m ÷ y^m = (x ÷ y)^m

Reason: a^m x b^m = (ab)^m

1. Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
2. Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).
3. Assertion (A) is true but Reason (R) is false.
4. Assertion (A) is false but Reason (R) is true.