In RD Sharma Solutions for Class 7 Chapter 6 Exponents, you will learn about a very important concept in mathematics known as exponents. This topic is also called powers, and it helps you to easily handle and work with large numbers by using a simple and clear method. RD Sharma Solutions Class 7 Maths Chapter 6 explains how exponents work and how they are useful in mathematics.
Do Check: RD Sharma Solutions for Class 7 Maths
What are Exponents?
Exponents are a shortcut to write repeated multiplication. Instead of writing 2 × 2 × 2, we can simply write it as 2³. Here, the number 2 is called the base and the number 3 is called the exponent. The exponent tells us how many times the base is multiplied by itself. Learning class 7 chapter 6 Exponents solutions helps you to solve complex problems quickly and easily.
Why Exponents are Important?
When you understand exponents properly, you can solve tough problems faster. RD Sharma Solutions for Class 7 Chapter 6 Exponents teaches you how to use exponents in algebra, geometry, and other math topics. This chapter explains everything step by step to make you confident with numbers and their powers.
Rules of Exponents in RD Sharma Solutions for Class 7 Chapter 6
RD Sharma Solutions for Class 7 Chapter 6 covers important rules, also called laws of exponents. These rules make your calculations easier:
- Product of Powers Rule: When bases are the same, add the exponents.
- Quotient of Powers Rule: When dividing bases, subtract the exponents.
- Power of a Power Rule: When a number is raised to another power, multiply the exponents.
Examples from Exponents Class 7 Chapter 6 Solutions
- 23 × 24 × 25 = 212 (add exponents)
- 512 ÷ 53 = 59 (subtract exponents)
- (72)3 = 76 (multiply exponents)
- (32)5 ÷ 34 = 36 (subtract exponents)
- 37 × 27 = 67 (multiply different bases but same exponents)
Access to Class 7 Maths Chapter 6 Exponents Solutions
Q1. Use of Exponent Laws to Simplify and Write in Exponential Form
2³ × 2⁴ × 2⁵
When multiplying numbers with the same base, we add their powers:
2³ × 2⁴ × 2⁵ = 23+4+5 = 212.
5¹² ÷ 5³
When dividing, subtract the exponents:
5¹² ÷ 5³ = 512-3 = 59.
(7²)³
Multiply powers when brackets are involved:
(7²)³ = 72×3 = 76.
(3²)⁵ ÷ 3⁴
Multiply powers inside brackets, then subtract:
3²⁵ ÷ 3⁴ = 310-4 = 36.
3⁷ × 2⁷
If exponents are same, multiply bases:
3⁷ × 2⁷ = (3×2)⁷ = 6⁷.
(5²¹ ÷ 5¹³) × 5⁷
Subtract powers then add:
5²¹ ÷ 5¹³ = 58,
5⁸ × 5⁷ = 58+7 = 515.
Q2. More Simplification with Exponents
{(2³)⁴ × 2⁸} ÷ 2¹²
Simplify powers first:
212+8-12 = 2⁸.
(8² × 8⁴) ÷ 8³
Add and subtract powers:
82+4-3 = 8³ = 2⁹.
(5⁷ ÷ 5²) × 5³
57-2+3 = 5⁸.
(5⁴ × x¹⁰y⁵) ÷ (5⁴ × x⁷y⁴)
Bases with same powers cancel out:
x10-7 y5-4 = x³y.
Q3. Simplification Using Power Rules
{(3²)³ × 2⁶} × 5⁶
3⁶ × 2⁶ × 5⁶ = (3×2×5)⁶ = 30⁶.
(x/y)¹² × y²⁴ × (2³)⁴
Simplify powers:
x¹² × y¹² × 2¹² = (2xy)¹².
(5/2)⁶ × (5/2)²
Add powers:
(5/2)8.
(2/3)⁵ × (3/5)⁵
Multiply fractions:
(2/5)⁵.
Q4. Convert 9×9×9×9×9 to Exponential Form with Base 3
9 is 3², so:
9⁵ = (3²)⁵ = 3¹⁰.
Q5. More Simplification Examples
(25)³ ÷ 5³
25 = 5²,
(5²)³ ÷ 5³ = 5⁶ ÷ 5³ = 5³.
(81)⁵ ÷ (32)⁵
81 = 3⁴, 32 = 2⁵:
(3⁴)⁵ ÷ (2⁵)⁵ = (3²⁰ ÷ 2²⁵) = (3/2)¹⁰.
9⁸ × (x²)⁵ ÷ 27⁴ × (x³)²
9 = 3², 27 = 3³:
3¹⁶ × x¹⁰ ÷ 3¹² × x⁶ = 3⁴ × x⁴ = (3x)⁴.
3² × 7⁸ × 13⁶ ÷ 2¹² × 9¹³
9 = 3²:
3² × 7⁸ × 13⁶ ÷ 2¹² × 3²⁶ = 7⁸ × 13⁶ ÷ 2¹² × 3²⁴.
Q6. Simplify These Expressions
(3⁵)¹¹ × (3¹⁵)⁴ – (3⁵)¹⁸ × (3⁵)⁵
First expression = 3¹¹⁵, second = 3¹¹⁵,
result = 0.
(16 × 2n+1 – 4 × 2n) ÷ (16 × 2n+2 – 2 × 2n+2)
Simplify:
2ⁿ(8-1)/2ⁿ(16-1) = 7/15.
(10 × 5n+1 + 25 × 5ⁿ) ÷ (3 × 5n+2 + 10 × 5n+1)
Simplify:
Answer = 3/5.
(16)⁷ × (25)⁵ × (81)³ ÷ (15)⁷ × (24)⁵ × (80)³
Simplify everything:
Final result = 2.
Q7. Find the Value of n
52n × 5³ = 5¹¹ => 2n + 3 = 11 ⇒ n = 4.
9 × 3ⁿ = 3⁷ => 3² × 3ⁿ = 3⁷ ⇒ n + 2 = 7 ⇒ n = 5.
8 × 2n+2 = 32 => 2³ × 2n+2 = 2⁵ ⇒ n + 5 = 5 ⇒ n = 0.
72n+1 ÷ 49 = 7³ => 72n+1-2 = 7³ ⇒ 2n - 1 = 3 ⇒ n = 2.
(3/2)⁴ × (3/2)⁵ = (3/2)2n+1 => 9 = 2n + 1 ⇒ n = 4.
(2/3)¹⁰ × ((3/2)²)⁵ = (2/3)2n-2
(2/3)10-10 = (2/3)2n-2 ⇒ 0 = 2n-2 ⇒ n = 1.