08-CBSE_Exponents & Powers-Test paper & Worksheet  

Introduction

Exponents and powers are used to represent repeated multiplication of a number by itself. For example, instead of writing 2 × 2 × 2 × 2, we can write 2^4.

What are Exponents?

An exponent is a small number that is raised to a power. It tells us how many times the base number should be multiplied by itself.

Laws of Exponents

There are several laws of exponents that help us simplify expressions with exponents:

1. Product Law: a^m × a^n = a^(m+n)

Example: 2^3 × 2^4 = 2^(3+4) = 2^7

2. Quotient Law: a^m ÷ a^n = a^(m-n)

Example: 2^5 ÷ 2^3 = 2^(5-3) = 2^2

3. Power Law: (a^m)^n = a^(mn)

Example: (2^3)^2 = 2^(3×2) = 2^6

Negative Exponents

A negative exponent means that the base number should be divided by itself as many times as the exponent indicates.

 Example: 2^(-3) = 1/2^3 = 1/8

 Fractional Exponents

A fractional exponent means that the base number should be raised to a power that is a fraction.

Example: 2^(1/2) = √2

 08-CBSE_Exponents & Powers-Test paper & Worksheet  

Simplifying Expressions with Exponents

To simplify an expression with exponents, we need to follow the order of operations (PEMDAS):

1. Evaluate any expressions inside parentheses.

2. Evaluate any exponents.

3. Evaluate any multiplication and division operations from left to right.

4. Evaluate any addition and subtraction operations from left to right.

 08-CBSE_Exponents & Powers-Test paper & Worksheet  

Examples

1. Simplify: 2^3 × 3^2

Answer: 2^3 × 3^2 = 8 × 9 = 72

2. Simplify: (2^2 × 3)^3

Answer: (2^2 × 3)^3 = (4 × 3)^3 = 12^3 = 1728

 

08-CBSE_Exponents & Powers-Test paper & Worksheet  

FAQs

1. What is an exponent?

An exponent is a small number that is raised to a power.

2. What is the product law of exponents?

The product law of exponents states that a^m × a^n = a^(m+n).

3. What is a negative exponent?

A negative exponent means that the base number should be divided by itself as many times as the exponent indicates.

 

08-CBSE_Exponents & Powers-Test paper & Worksheet  

Practice Questions

1. Simplify: 2^4 × 3^2

2. Simplify: (2^3 × 3)^2

3. Simplify: 2^(-2) × 3^2

4. Simplify: (2^2 × 3)^(-1)

5. Simplify: 2^(1/2) × 3^(1/2)

08-CBSE_Exponents & Powers-Test paper & Worksheet  - Test paper

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