Exponents Worksheet for Class 6: Whole Number, Negative & Zero Exponents

To solve a negative exponent, you find the reciprocal of the base and change the exponent to a positive number. The general rule is written as a⁻ⁿ = 1/aⁿ, where 'a' is a non-zero number.

Here is a step-by-step example:

• To solve 4⁻², you first write its reciprocal: 1/4².
• Next, you calculate the value of the power in the denominator: 4² = 16.
• Therefore, 4⁻² = 1/16.

For Grade 6, the main laws of exponents focus on how to handle operations with powers that have the same base. These rules are essential for simplifying expressions and solving problems.

The key rules include:

• Product Law: When multiplying powers with the same base, add the exponents. For example, aᵐ × aⁿ = aᵐ⁺ⁿ.
• Quotient Law: When dividing powers with the same base, subtract the exponents. For example, aᵐ ÷ aⁿ = aᵐ⁻ⁿ.
• Zero Exponent Rule: Any non-zero base raised to the power of zero equals 1. For example, a⁰ = 1.
• Negative Exponent Rule: A negative exponent means to take the reciprocal. For example, a⁻ⁿ = 1/aⁿ.

In an expression like 5³, the base and the exponent are two different parts that tell you how to perform a calculation. Understanding this difference is the first step in learning about powers.

• The base is the number that is being multiplied by itself. In 5³, the base is 5.
• The exponent (or power) is the small number written above and to the right of the base. It tells you how many times to multiply the base by itself. In 5³, the exponent is 3, so you calculate 5 × 5 × 5.

This exponent worksheet for Class 6 is designed to help you master the rules of exponents through structured practice. It reinforces learning, improves problem-solving speed, and builds confidence for exams.

Benefits include:

• Concept Reinforcement: It provides targeted practice on whole number bases, negative exponents, and the zero exponent rule.
• Stepwise Practice: The questions are laid out clearly to help you practice calculations step by step.
• Exam Preparation: It includes question types like 'evaluate', 'fill in the blanks', and 'true/false', which are common in school exams.
• Easy Revision: As a printable exponent worksheet PDF, it is perfect for quick revision at home.

To evaluate an exponential expression means to find its final numerical value by carrying out the multiplication indicated by the exponent. This involves expanding the expression and then simplifying it.

For example, to evaluate 2⁵:

• Identify the base (2) and the exponent (5).
• Write out the multiplication: 2 × 2 × 2 × 2 × 2.
• Calculate the final answer: 32.

Any non-zero number with a zero exponent equals 1 because of the quotient law of exponents. This rule helps keep the laws of exponents consistent and logical.

Consider the expression aᵐ / aⁿ = aᵐ⁻ⁿ. If we let m = n, then:

• The expression becomes aⁿ / aⁿ. Any number divided by itself is 1.
• Using the rule, it also becomes aⁿ⁻ⁿ = a⁰.
• Since both results must be equal, we can conclude that a⁰ = 1.

Yes, this exponents worksheet PDF with answers includes a complete answer key. The solutions are provided with stepwise explanations to help students check their work and understand the correct method for solving each problem.

Having an answer key is useful for:

• Independent learning and self-assessment.
• Parents who want to help their children with homework.
• Quick and effective revision before an exam.

Any expression with a base of one will always result in an answer of 1, regardless of the exponent. This is because you are multiplying 1 by itself a certain number of times.

For example:

• 1² = 1 × 1 = 1
• 1¹⁰ = 1 × 1 × ... (10 times) = 1
• 1⁻⁵ = 1/1⁵ = 1/1 = 1

Yes, this is a printable exponent worksheet designed in a print-friendly PDF format. You can easily download and print it for use in the classroom, for homework, or for extra practice at home. Its clear layout and readable font make it ideal for Grade 6 students to work on paper.