Ncert solutions mathematics class 7 Solutions for Chapter 13 exponents and powers

Find the value of:

2^6

Find the Value of:

11^2

Q1) Find the value of:

(i) 2^6

(ii) 9^3

(iii) 11^2

(iv) 5^4

Find the Value of:

9^3

Find the Value of:

5^4

Q2) Express the following in exponential form:

(i) 6\times6\times6\times6

(ii) t\times t

(iii) b\times b\times b\times b

(iv) 5\times5\times7\times7\times7

(v) 2\times2\times a\times a

(vi) a\times a\times a\times c\times c\times c\times c\times d

Express the following in Exponential form:

a × a × a × c × c × c × c × d

Express the following in Exponential form:

5 × 5× 7 × 7 × 7

Express the following in Exponential form:

6 × 6 × 6 × 6

Express the following in Exponential form:

t × t

Express the following in Exponential form:

b × b × b × b

Express each of the following Numbers using Exponential Notation:

3125

Express each of the following Numbers using Exponential Notation:

512

Express each of the following Numbers using Exponential Notation:

729

Express each of the following Numbers using Exponential Notation:

343

Q3) Express each of the following numbers using the exponential notation:

(i) 512 (ii) 343 (iii) 729 (iv) 3125

Identify the greater number, wherever possible, in each of the following?

2^8 OR 8^2

Identify the greater number, wherever possible, in each of the following?

5^3 OR 3^5

Identify the greater number, wherever possible, in each of the following?

2^{10} OR 10^2

Identify the greater number, wherever possible, in each of the following?

100^2 OR 2^{100}

Identify the greater number, wherever possible, in each of the following?

4^3 OR 3^4

Q4) Identify the greater number, wherever possible, in each of the following?

(i) 4^{3\ } or 3^4

(ii) 5^3 or 3^5

(iii) 2^8 or 8^2

(iv) 100^2 or 2^{100}

(v) 2^{10} or 10^2

Q5) Express each of the following as product of powers of their prime factors:

(i) 648 (ii) 405 (iii) 540 (iv) 3,600

Express each of the following as Product of Powers of their Prime Factors:

540

Express each of the following as Product of Powers of their Prime Factors:

3,600

Express each of the following as Product of Powers of their Prime Factors:

405

Express each of the following as Product of Powers of their Prime Factors:

648

Q6) Simplify:

(i) 2\times10^3

(ii) 7^2\times2^2

(iii) 2^3\times5

(iv) 3\times4^4

(v) 0\times10^2

(vi) 5^2\times3^3

(vii) 2^4\times3^2

(viii) 3^2\times10^4

Simplify:

3 x 4^4

Simplify:

0 x 10^2

Simplify:

2^3 x 5

Simplify:

2 × 10^{^3}

Simplify:

7^2 x 2^2

Simplify:

5^2 x 3^3

Simplify:

2^4 x 3^2

Simplify:

3^2 x 10^4

Simplify:

\left(-4\right)^3

Q7) Simplify:

(i) \left(-4\right)^3

(ii) \left(-3\right)\times\left(-2\right)^3

(iii) \left(-3\right)^2\times\left(-5\right)^2

(iv) \left(-2\right)^3\times\left(-10\right)^3

Simplify:

\left(-3\right)^2 x \left(-5\right)^2

Simplify:

\left(-2\right)^3 x \left(-10\right)^3

Simplify:

(–3) × \left(-2\right)^3

Q8) Compare the following numbers:

(i) 2.7\times10^{12};\ 1.5\times10^8

(ii) 4\times10^{14};\ 3\times10^{17}

Compare the following numbers:

4 x 10^{14} ; 3 x 10^{^{17}}

Compare the following numbers:

2.7 × 10^{12} ; 1.5 x 10^8

Using laws of exponents, simplify and write the answer in exponential form:

\left(5^2\right)^3 ÷ 5^3

Using laws of exponents, simplify and write the answer in exponential form:

7^X x 7^{^2}

Using laws of exponents, simplify and write the answer in exponential form:

6^{15} ÷ 6^{10}

Using laws of exponents, simplify and write the answer in exponential form:

a^3 x a^2

Using laws of exponents, simplify and write the answer in exponential form:

3^{2\ } x 3^4 x 3^8

Using laws of exponents, simplify and write the answer in exponential form:

\left(3^4\right)^3

Using laws of exponents, simplify and write the answer in exponential form:

\left(2^{20}\div2^{15}\right)\ x\ 2^3

Using laws of exponents, simplify and write the answer in exponential form:

8^t ÷ 8^2

Q1) Using laws of exponents, simplify and write the answer in exponential form:

(i) 3^2\times3^4\times3^8

(ii) 6^{15}\div6^{10}

(iii) a^3\times a^2

(iv) 7^x\times7^2

(v) \left(5^2\right)^3\div5^3

(vi) 2^5\times5^5

(vii) a^4\times b^4

(viii) \left(3^4\right)^3

(ix) \left(2^{20}\div2^{15}\right)\times2^3

(x)8^t\div8^2

Using laws of exponents, simplify and write the answer in exponential form:

a^4 x b^4

Using laws of exponents, simplify and write the answer in exponential form:

2^5 x 5^5

Simplify and express each of the following in exponential form:

25^4\div5^3

Q2) Simplify and express each of the following in exponential form:

(i) \frac{2^3\times3^4\times4}{3\times32}

(ii) \left[\left(5^2\right)^{3\ }\times5^4\right]\div5^7

(iii) \left(25^4\div5^3\right)

(iv) \frac{3\times7^2\times11^8}{21\times11^3}

(v) \frac{3^7}{3^4\times3^3}

(vi) 2^0+3^0+4^0

(vii) 2^0\times3^0\times4^0

(viii) \left(3^0+2^0\right)\times5^0

(ix) \frac{2^8\times a^5}{4^3\times a3}

(x) \left(\frac{a^5}{a^3}\right)\times a^8

(xi) \frac{4^5\times a^8b^3}{4^5\times a^5b^2}

(xii) \left(2^3\times2\right)^2

Simplify and express each of the following in exponential form:

(2^3\times3^4\times4)/(3\times32)

Simplify and express each of the following in exponential form:

(3\times7^2\times11^8)/(21\times11^3)

Simplify and express each of the following in exponential form:

3^7/(3^4\times3^3)

Simplify and express each of the following in exponential form:

2^0+3^0+4^0

Simplify and express each of the following in exponential form:

2^0\times3^0\times4^0

Simplify and express each of the following in exponential form:

(3^0+2^0)\times5^0

Simplify and express each of the following in exponential form:

(2^8\times a^5)/(4^3\times a^3)

Simplify and express each of the following in exponential form:

(a^5/a^3)\times a^8

Simplify and express each of the following in exponential form:

(4^5\times a^8b^3)/(4^5\times a^5b^2)

Simplify and express each of the following in exponential form:

(2^3\times2)^2

Say True or False and Justify your answer:

10\times10^{11}=100^{11}

Say True or False and Justify your answer:

2^3>5^2

Say True or False and Justify your answer:

3^0=(1000)^0

Say True or False and Justify your answer:

2^3\times3^2=6^5

Q3) Say true or false and justify your answer:

(i) 10\times10^{11}=100^{11}

(ii) 2^3>5^2

(iii) 2^3\times3^2=6^5

(iv) 3^0=\left(1000\right)^0

Express each of the following as a product of prime factors only in exponential form:

729 × 64

Q4) Express each of the following as a product of prime factors only in exponential form:

(i) 108\times192

(ii) 270

(iii) 729\times64

(iv) 768

Simplify and express each of the following in exponential form:

((5^2)^3\times5^4)\div5^7

Express each of the following as a product of prime factors only in exponential form:

270

Express each of the following as a product of prime factors only in exponential form:

108 × 192

Express each of the following as a product of prime factors only in exponential form:

768

Simplify:

(25\times5^2\times t^8)/(10^3\times t^4)

Simplify:

((2^5)^2\times7^3)\ /\ (8^3\times7)

Q5) Simplify:

(i) \frac{\left(2^5\right)^2\times7^3}{8^3\times7}

(ii) \frac{25\times5^2\times t^3}{10^3\times t^4}

(iii) \frac{3^5\times10^5\times25}{5^7\times6^5}

Simplify:

(3^5\times10^5\times25)/(5^7\times6^5)

Write the following numbers in the Expanded forms:

279404

Write the following numbers in the Expanded forms:

120719

Write the following numbers in the Expanded forms:

3006194

Write the following numbers in the Expanded forms:

20068

Write the following numbers in the Expanded forms:

2806196

Q1) Write the following numbers in the expanded forms:

(i) 2,79,404

(ii) 30,06,194

(iii) 28,06,196

(iv) 1,20,719

(v) 20,068

Find the number from each of the following Expanded forms:

\left(3×10\right)^4+\left(7×10\right)^2+\left(5×10\right)^0

Find the number from each of the following Expanded forms:

\left(8×10\right)^4+\left(6×10\right)^3+\left(0x10\right)^2+\left(4×10\right)^1+\left(5×10\right)^0

Q2) Find the number from each of the following expanded forms:

(a) 8\times10^4+6\times10^3+0\times10^2+4\times10^1+5\times10^6

(b) 4\times10^4+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

Find the number from each of the following Expanded forms:

\left(4×10\right)^5+\left(5×10\right)^3+\left(3×10\right)^2+\left(2×10\right)^0

Find the number from each of the following Expanded forms:

\left(9×10\right)^5+\left(2×10\right)^2+\left(3×10\right)^1

Express the following numbers in Standard form:

5,00,00,000

Q3) 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

Express the following numbers in Standard form:

39087.8

Express the following numbers in Standard form:

3,18,65,00,000

Express the following numbers in Standard form:

70,00,000

Express the following numbers in Standard form:

3,90,878

Express the following numbers in Standard form:

3908.78

Q4) Express the number appearing in the following statements in standard form.

(a) The distance between Earth and Moon is 384,000,000 m.

(b) Speed of light in vacuum is 300,000,000 m/s.

(c) Diameter of the Earth is 1,27,56,000 m.

(d) Diameter of the Sun is 1,400,000,000 m.

(e) In a galaxy there are on an average 100,000,000,000 stars.

(f) The universe is estimated to be about 12,000,000,000 years old.

(g) The distance of the Sun from the centre of the Milky Way Galaxy is estimated to

be 300,000,000,000,000,000,000 m.

(h) 60,230,000,000,000,000,000,000 molecules are contained in a drop of water

weighing 1.8 gm.

(i) The earth has 1,353,000,000 cubic km of sea water.

(j) The population of India was about 1,027,000,000 in March, 2001.

Express the number appearing in the following statements in standard form.

The distance between Earth and Moon is 384,000,000 m.

Express the number appearing in the following statements in standard form.

Speed of light in vacuum is 300,000,000 m/s.

Express the number appearing in the following statements in standard form.

Diameter of the Earth is 1,27,56,000 m.

Express the number appearing in the following statements in standard form.

Diameter of the Sun is 1,400,000,000 m.

Express the number appearing in the following statements in standard form.

In a galaxy there are on an average 100,000,000,000 stars.

Express the number appearing in the following statements in standard form.

The universe is estimated to be about 12,000,000,000 years old.

Express the number appearing in the following statements in standard form.

60,230,000,000,000,000,000,000 molecules are contained in a drop of water

weighing 1.8 gm.

Express the number appearing in the following statements in standard form.

The earth has 1,353,000,000 cubic km of sea water.

Express the number appearing in the following statements in standard form.

The distance of the Sun from the centre of the Milky Way Galaxy is estimated to be

300,000,000,000,000,000,000 m.

Express the number appearing in the following statements in standard form.

The population of India was about 1,027,000,000 in March, 2001.