Q: Exercise 11.1 asks students to evaluate powers, express repeated products in exponential form, write numbers as powers, express numbers as products of prime factors in exponential form, simplify expressions using powers, evaluate powers with negative bases and compare large numbers written in standard form.

1. (i) 64 (ii) 729 (iii) 121 (iv) 625. 2. (i) 64 (ii) $t^2$ (iii) $b^4$ (iv) $5^2\times7^3$ (v) $2^2\times a^2$ (vi) $a^3\times c^4\times d$. 3. (i) $2^9$ (ii) $7^3$ (iii) $3^6$ (iv) $5^5$. 4. (i) $3^4$ (ii) $3^5$ (iii) $2^8$ (iv) $2^{100}$ (v) $2^{10}$. 5. (i) $2^3\times3^4$ (ii) $5\times3^4$ (iii) $2^2\times3^3\times5$ (iv) $2^4\times3^2\times5^2$. 6. (i) 2000 (ii) 196 (iii) 40 (iv) 768 (v) 0 (vi) 675 (vii) 144 (viii) 90000. 7. (i) $-64$ (ii) 24 (iii) 225 (iv) 8000. 8. (i) $2.7\times10^{12}>1.5\times10^8$ (ii) $4\times10^{14}<3\times10^{17}$.

Q: 1. Write the following numbers in the expanded forms: 279404, 3006194, 2806196, 120719, 20068. 2. Find the number from each of the following expanded forms: (a) $8\times10^4+6\times10^3+0\times10^2+4\times10^1+5\times10^0$ (b) $4\times10^5+5\times10^3+3\times10^2+2\times10^0$ (c) $3\times10^4+7\times10^2+5\times10^0$ (d) $9\times10^5+2\times10^2+3\times10^1$. 3. Express the following numbers in standard form: (i) 5,00,00,000 (ii) 70,00,000 (iii) 3,18,65,00,000 (iv) 3,90,878 (v) 39087.8 (vi) 3908.78. 4. Express the number appearing in the following statements in standard form, including distances, speed of light, diameters of Earth and Sun, number of stars, age of universe, distance of Sun from Milky Way centre, molecules in a drop of water, sea-water volume and population of India.

1. $279404=2\times10^5+7\times10^4+9\times10^3+4\times10^2+0\times10^1+4\times10^0$; $3006194=3\times10^6+0\times10^5+0\times10^4+6\times10^3+1\times10^2+9\times10^1+4\times10^0$; $2806196=2\times10^6+8\times10^5+0\times10^4+6\times10^3+1\times10^2+9\times10^1+6\times10^0$; $120719=1\times10^5+2\times10^4+0\times10^3+7\times10^2+1\times10^1+9\times10^0$; $20068=2\times10^4+0\times10^3+0\times10^2+6\times10^1+8\times10^0$. 2. (a) 86045 (b) 405302 (c) 30705 (d) 900230. 3. (i) $5\times10^7$ (ii) $7\times10^6$ (iii) $3.1865\times10^9$ (iv) $3.90878\times10^5$ (v) $3.90878\times10^4$ (vi) $3.90878\times10^3$. 4. (a) $3.84\times10^8$ m (b) $3\times10^8$ m/s (c) $1.2756\times10^7$ m (d) $1.4\times10^9$ m (e) $1\times10^{11}$ (f) $1.2\times10^{10}$ years (g) $3\times10^{20}$ m (h) $6.023\times10^{22}$ (i) $1.353\times10^9\text{ km}^3$ (j) $1.027\times10^9$.

Question 1

Exercise 11.1 asks students to evaluate powers, express repeated products in exponential form, write numbers as powers, express numbers as products of prime factors in exponential form, simplify expressions using powers, evaluate powers with negative bases and compare large numbers written in standard form.

Accepted Answer

1. (i) 64 (ii) 729 (iii) 121 (iv) 625.
2. (i) 64 (ii)

$t^2$

(iii)

$b^4$

(iv)

5^2\times7^3

(v)

2^2\times a^2

(vi)

a^3\times c^4\times d

.
3. (i)

$2^9$

(ii)

$7^3$

(iii)

$3^6$

(iv)

$5^5$

.
4. (i)

$3^4$

(ii)

$3^5$

(iii)

$2^8$

(iv)

2^{100}

(v)

2^{10}

.
5. (i)

2^3\times3^4

(ii)

5\times3^4

(iii)

2^2\times3^3\times5

(iv)

2^4\times3^2\times5^2

.
6. (i) 2000 (ii) 196 (iii) 40 (iv) 768 (v) 0 (vi) 675 (vii) 144 (viii) 90000.
7. (i)

$-64$

(ii) 24 (iii) 225 (iv) 8000.
8. (i)

2.7\times10^{12}>1.5\times10^8

(ii)

4\times10^{14}<3\times10^{17}

.

Question 2

Exercise 11.2 asks students to simplify expressions using laws of exponents, say true or false with justification, express products in prime-factor exponential form and simplify expressions involving powers and variables.

Accepted Answer

1. (i) $3^{14}$ (ii) $6^5$ (iii) $a^5$ (iv) $7^{x+2}$ (v) $5^3$ (vi) $10^5$ (vii) $(ab)^4$ (viii) $3^{12}$ (ix) $2^8$ (x) $8^{t-2}$. 2. (i) $3^3$ (ii) $5^3$ (iii) $5^5$ (iv) $7	imes11^5$ (v) $3^0$ or 1 (vi) 3 (vii) 1 (viii) 2 (ix) $(2a)^2$ (x) $a^{10}$ (xi) $a^3b$ (xii) $2^8$. 3. (i) False; $10	imes10^{11}=10^{12}$ and $(100)^{11}=10^{22}$ (ii) False; $2^3=8$, $5^2=25$ (iii) False; $6^5=2^5	imes3^5$ (iv) True; $3^0=1$, $(1000)^0=1$. 4. (i) $2^8	imes3^4$ (ii) $2	imes3^3	imes5$ (iii) $3^6	imes2^6$ (iv) $2^8	imes3$. 5. (i) 98 (ii) $\frac{4}{5t^8}$ (iii) 1.

Question 3

1. Write the following numbers in the expanded forms: 279404, 3006194, 2806196, 120719, 20068. 2. Find the number from each of the following expanded forms: (a) $8	imes10^4+6	imes10^3+0	imes10^2+4	imes10^1+5	imes10^0$ (b) $4	imes10^5+5	imes10^3+3	imes10^2+2	imes10^0$ (c) $3	imes10^4+7	imes10^2+5	imes10^0$ (d) $9	imes10^5+2	imes10^2+3	imes10^1$. 3. Express the following numbers in standard form: (i) 5,00,00,000 (ii) 70,00,000 (iii) 3,18,65,00,000 (iv) 3,90,878 (v) 39087.8 (vi) 3908.78. 4. Express the number appearing in the following statements in standard form, including distances, speed of light, diameters of Earth and Sun, number of stars, age of universe, distance of Sun from Milky Way centre, molecules in a drop of water, sea-water volume and population of India.

Accepted Answer

1. $279404=2	imes10^5+7	imes10^4+9	imes10^3+4	imes10^2+0	imes10^1+4	imes10^0$; $3006194=3	imes10^6+0	imes10^5+0	imes10^4+6	imes10^3+1	imes10^2+9	imes10^1+4	imes10^0$; $2806196=2	imes10^6+8	imes10^5+0	imes10^4+6	imes10^3+1	imes10^2+9	imes10^1+6	imes10^0$; $120719=1	imes10^5+2	imes10^4+0	imes10^3+7	imes10^2+1	imes10^1+9	imes10^0$; $20068=2	imes10^4+0	imes10^3+0	imes10^2+6	imes10^1+8	imes10^0$. 2. (a) 86045 (b) 405302 (c) 30705 (d) 900230. 3. (i) $5	imes10^7$ (ii) $7	imes10^6$ (iii) $3.1865	imes10^9$ (iv) $3.90878	imes10^5$ (v) $3.90878	imes10^4$ (vi) $3.90878	imes10^3$. 4. (a) $3.84	imes10^8$ m (b) $3	imes10^8$ m/s (c) $1.2756	imes10^7$ m (d) $1.4	imes10^9$ m (e) $1	imes10^{11}$ (f) $1.2	imes10^{10}$ years (g) $3	imes10^{20}$ m (h) $6.023	imes10^{22}$ (i) $1.353	imes10^9	ext{ km}^3$ (j) $1.027	imes10^9$.