NCERT Solutions for Class 7 Clat Chapter 13 Exponents And Powers

Find the value of:

(i) 2⁶ (ii) 9³

(iii) 11² (iv)5⁴

Express the following in exponential form:

(i) 6 × 6 × 6 × 6 (ii) t × t

(iii) b × b × b × b (iv) 5 × 5 × 7 ×7 × 7

(v) 2 × 2 × a × a (vi) a × a × a × c × c × c × c × d

Express the following numbers using exponential notation:

(i) 512 (ii) 343

(iii) 729 (iv) 3125

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

(i) 4³ or 3⁴ (ii) 5³ or 3⁵

(iii) 2⁸ or 8² (iv) 100² or 2¹⁰⁰

(v) 2¹⁰ or 10²

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

(i) 648 (ii) 405

(iii) 540 (iv) 3,600

Simplify:

(i) 2 × 10³ (ii) 7² × 2²

(iii) 2³ × 5 (iv) 3 × 4⁴

(v) 0 × 10² _­­­­­ (vi) 5² × 3³

(vii) 2⁴ × 3² (viii) 3² × 10⁴

Simplify:

(i) (− 4)³ 

(ii) (− 3) × (− 2)³

(iii) (− 3)² × (− 5)² 

(iv)(− 2)³ × (−10)³

Compare the following numbers:

(i) 2.7 × 10¹²; 1.5 × 10⁸

(ii) 4 × 10¹⁴; 3 × 10¹⁷

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

(i) 3² × 3⁴ × 3⁸ (ii) 6¹⁵ ÷ 6¹⁰ (iii) a³ × a²

(iv) 7^x× 7² (v) $5^{2^3}÷5^3$ (vi) 2⁵ × 5⁵

(vii) a⁴ × b⁴ (viii) (3⁴)³

(ix) $\left(2^{20}÷2^{15}\right)\times 2^3$ (x) 8^t ÷ 8²

Simplify and express each of the following in exponential form:

(i) $\frac{2^3\times 3^4\times 4}{3\times 32}$ (ii) $\left[{5^2}^3\times 5^4\right]÷5^7$ (iii) ${25}^4÷5^3$

(iv) $\frac{3\times 7^2\times {11}^8}{21\times {11}^3}$ (v) $\frac{3^7}{3^{4\times }{3}^3}$ (vi) 2⁰ + 3⁰ + 4⁰

(vii) 2⁰ × 3⁰ × 4⁰ (viii) (3⁰ + 2⁰) × 5⁰ (ix) $\frac{2^8\times a^5}{4^3\times a^3}$

(x) $\left(\frac{a^5}{a^3}\right)\times a^8$ (xi) $\frac{4^5\times a^8{b}^3}{4^5\times a^5\times b^2}$ (xii) ${\left(2^3\times 2\right)}^2$