Power and Surds Notes for SSC Exams 2026

Power and Surds, also called Indices, are a key topic in the SSC exam mathematics and form the foundation for many advanced problems in Algebra, Arithmetic, and Reasoning. Mastering powers and surds is essential for solving questions quickly, accurately, and with confidence. Check all the fundamental rules, such as multiplication and division of powers, power of a power, zero exponent, equality rules, and surds (roots).

Along with these concepts, the notes provide effective exam strategies, including daily full-length mocks, mini-mocks for focused practice, prioritizing important topics like Current Affairs and Static GK, and relying on book-based study for better understanding. Multiple worked examples are included to show practical application, helping students learn how to approach and solve questions step by step. By following this guide, SSC aspirants can strengthen their problem-solving skills, improve speed, and revise efficiently, ensuring they are fully prepared for SSC Exams 2026.

Power and Surds 

Power and Surds, also known as Indices, form a foundational topic for competitive exams like SSC. Mastering these concepts is crucial for efficient problem-solving and achieving higher scores. This blog delves into the core rules governing powers and surds, offers strategic insights for exam preparation, and illustrates practical applications through solved examples, ensuring a comprehensive understanding.

Fundamental Rules of Powers and Surds

The foundational concept is that if a number a is multiplied by itself n times (a * a * a * ... n times), it can be expressed as aⁿ, where a is the base and n is the power (or exponent).

The key operational rules are as follows:

1. Multiplication with Common Base: When multiplying two exponential terms with the same base, their powers are added.

• aᵐ * aⁿ = aᵐ⁺ⁿ

2. Division with Common Base: When dividing two exponential terms with the same base, their powers are subtracted.

• aᵐ / aⁿ = aᵐ⁻ⁿ

3. Power of a Power (with Brackets): If an exponential term is raised to another power, the powers are multiplied. This applies when brackets are used to group the exponents.

• (aᵐ)ⁿᵖ = aᵐ*ⁿ*ᵖ

4. Power of a Power (without Brackets): If there are no brackets, the expression is evaluated from the top down. This is fundamentally different from the rule with brackets.

• aᵐⁿᵖ ≠ aᵐ*ⁿ*ᵖ

5. Zero Exponent Rule: Any number raised to the power of zero equals 1.

• a⁰ = 1

• ( Remember 'universality': no matter how complex the base, if the exponent is zero, the result is always 1.)

6. Equality with Common Base: If two exponential expressions are equal and their bases are the same, then their exponents must also be equal.

• If aˣ = aʸ, then x = y.

7. Equality with Common Exponent: If two exponential expressions are equal and their exponents are the same, then their bases must also be equal.

• If aˣ = bˣ, then a = b.

8. The Rule of Surds (Roots): The n-th root of a number 'a can be expressed as 'a raised to the power of 1/n.

• ⁿ√a = a¹/ⁿ

Exam Preparation Strategy

Effective preparation is key for competitive exams. Follow these strategic guidelines:

1. Daily Mock Tests: Taking one full mock test daily is the single most important activity.

• Do not be discouraged by low scores initially. The goal of the first 20 mocks is to build familiarity and analyze mistakes, not just to score high. Consistent practice will naturally improve performance.

• Mocks develop crucial skills like time management and the ability to solve problems using options.

2. Utilize Mini Mocks: When short on time (10-15 minutes), use Mini Mocks. These are effective for targeted practice on specific topics such as Current Affairs, Static GK, or individual Math chapters.

3. Prioritize Key Subjects: For the General Knowledge/General Studies (GK/GS) section, give special focus to:

• Current Affairs (CA)

• Static GK

• Recent exam analysis shows these areas have the highest weightage. If subjects like History and Polity are already studied, revise them through mocks instead of re-studying entire subjects.

4. Emphasize Book-Based Study: Rely on books, especially those based on Previous Year Questions (PYQs). Spending excessive hours only watching online classes without self-study from books is an ineffective strategy.

5. Consistent Revision: Maths and Reasoning are subjects easily forgotten without practice. Regular revision is essential. Daily mocks and mini-mocks can effectively maintain constant practice.

Worked Examples

Applying the rules of powers and surds to solve problems is crucial for exam success.

Problem 1

Find the value of: 15^(0.64) * 15^(0.36)

• Solution: Since bases are same, add exponents: 15^(0.64 + 0.36) = 15¹.

• Answer: 15

Problem 2

Find the value of: 256^(0.15) * 16^(0.20)

• Solution: Make bases common: 256 = 16². So, (16²)^(0.15) * 16^(0.20) = 16^(2 * 0.15) * 16^(0.20) = 16^(0.30) * 16^(0.20). Add exponents: 16^(0.30 + 0.20) = 16^(0.50) = 16^(1/2) = √16 = 4.

• Answer: 4

Problem 3

If 625^(2x - 3) = 25⁶¹⁶¹⁰, find the value of x.

• Solution: Simplify right side: 25⁶¹⁶¹⁰ = 25⁶ (any number to power 0 is 1, so 1610^0 becomes 1. This means 6^1=6). Make bases common: 625 = 25². So, (25²)^(2x - 3) = 25⁶. This becomes 25^(4x - 6) = 25⁶. Equate exponents: 4x - 6 = 6, so 4x = 12, x = 3.

• Answer: 3

Problem 4

Simplify: [(-1/2)²]⁻²⁻¹

• Solution: Multiply all exponents: 2 * (-2) * (-1) = 4. So, (-1/2)⁴ = (-1)⁴ / 2⁴ = 1 / 16.

• Answer: 1/16

Problem 5

Simplify: ⁵√[x⁻³/⁵]⁻⁵/³ raised to the power of 5.

• Solution: Convert ⁵√ to ( )^(1/5). The expression is ( ( (x⁻³/⁵)¹/⁵ )⁻⁵/³ )⁵. Multiply all exponents: (-3/5) * (1/5) * (-5/3) * 5. This product simplifies to 1. So the result is x¹.

• Answer: x

Problem 6

Simplify: 8 - [4⁹/⁴ * √(2 * 2²)] / [2 * √2⁻²] all raised to the power 1/2.

• Solution:

• Numerator: 4⁹/⁴ * √(2 * 2²) = (2²)⁹/⁴ * √2³ = 2⁹/² * 2³/² = 2^(9/2 + 3/2) = 2^(12/2) = 2⁶.

• Denominator: 2 * √2⁻² = 2 * (2⁻²)¹/² = 2 * 2⁻¹ = 2¹ * 2⁻¹ = 2⁰ = 1.

• The fraction simplifies to 2⁶ / 1 = 64.

• The expression inside the main bracket is 64.

• The lecturer's conclusion for the entire bracketed term simplifies to 8.

• So, 8 - 8 = 0.

• Answer (as per lecture conclusion): 0

Problem 7

Find the square root of 0.444...

• Solution:

• Convert recurring decimal to fraction: 0.444... = 0.4̅ = 4/9.

• Find the square root: √(4/9) = √4 / √9 = 2/3.

• Convert back to decimal: 2/3 = 0.666....

• Answer: 0.666...

Problem 8

Find the value of 'm' if (10/11)⁷ * (11/10)¹⁰ * (11/10)⁹ = (10/11)³ᵐ⁺¹⁷

• Solution: Make all bases (10/11).

• (11/10)¹⁰ becomes (10/11)⁻¹⁰.

• (11/10)⁹ becomes (10/11)⁻⁹.

• Equation becomes: (10/11)⁷ * (10/11)⁻¹⁰ * (10/11)⁻⁹ = (10/11)³ᵐ⁺¹⁷.

• Add exponents on left: 7 - 10 - 9 = -12.

• So, (10/11)⁻¹² = (10/11)³ᵐ⁺¹⁷.

• Equate exponents: -12 = 3m + 17.

• 3m = -12 - 17 = -29.

• m = -29/3.

• Answer: -29/3