Understanding Exponents and Power in Class 7 Maths CBSE

Oct 13, 2025 by magicalceylontours.com 33 views

Simplify 36×p⁸×6⁵/6×z³ Chapter Exponents and Power Class 7 Maths CBSE

Understanding Exponents and Power in Class 7 Maths CBSE

In the world of mathematics, exponents and power play a vital role in simplifying complex expressions. The concept of exponents and power is introduced in class 7 maths CBSE, and it's essential to grasp this concept to solve various mathematical problems. In this article, we will simplify the expression 36×p⁸×6⁵/6×z³ and explore the concept of exponents and power in detail.

What are Exponents and Power?

Exponents and power are used to represent repeated multiplication of a number. In other words, exponents and power are a shorthand way of writing repeated multiplication. For example, 2³ can be written as 2×2×2, which means 2 multiplied by itself three times. The exponent 3 represents the number of times the base 2 is multiplied.

Simplifying Exponents and Power

To simplify exponents and power, we need to follow the order of operations (PEMDAS):

Parentheses: Evaluate expressions inside parentheses first.
Exponents: Evaluate any exponential expressions next.
Multiplication and Division: Evaluate multiplication and division operations from left to right.
Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Simplifying the Expression 36×p⁸×6⁵/6×z³

To simplify the expression 36×p⁸×6⁵/6×z³, we need to follow the order of operations:

Evaluate the exponents:
- 36 can be written as 6²
- 6⁵ can be written as (6²)³
- p⁸ remains the same
- z³ remains the same
Simplify the expression:
- 36×p⁸×6⁵/6×z³ = (6²)×p⁸×(6²)³/6×z³
- = 6²×p⁸×6⁶/6×z³
- = 6²×p⁸×6⁵/6×z³ (since 6⁶ = 6⁵×6)
- = 6×p⁸×6⁵/6×z³ (since 6² = 6×6)
- = p⁸×6⁵/z³ (since 6/6 = 1)
Simplify further:
- p⁸×6⁵/z³ = p⁸×(6²)²/z³
- = p⁸×36²/z³
- = p⁸×1296/z³

Conclusion

In conclusion, simplifying exponents and power in class 7 maths CBSE requires a thorough understanding of the concept. By following the order of operations and simplifying the expression step by step, we can simplify the expression 36×p⁸×6⁵/6×z³ to p⁸×1296/z³. This article has provided a detailed explanation of the concept of exponents and power and has simplified a complex expression using this concept.

Key Takeaways

Exponents and power are used to represent repeated multiplication of a number.
To simplify exponents and power, we need to follow the order of operations (PEMDAS).
Simplifying the expression 36×p⁸×6⁵/6×z³ requires evaluating the exponents and simplifying the expression step by step.

Frequently Asked Questions

What is the order of operations in mathematics?
How do we simplify exponents and power in class 7 maths CBSE?
What is the final simplified expression for 36×p⁸×6⁵/6×z³?

Answer

The order of operations in mathematics is PEMDAS: Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction.
To simplify exponents and power in class 7 maths CBSE, we need to follow the order of operations and simplify the expression step by step.
The final simplified expression for 36×p⁸×6⁵/6×z³ is p⁸×1296/z³.
Frequently Asked Questions (FAQs) on Simplifying Exponents and Power in Class 7 Maths CBSE

Q: What is the order of operations in mathematics?

A: The order of operations in mathematics is PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction. This order of operations helps us to simplify complex mathematical expressions by following a specific sequence.

Q: How do we simplify exponents and power in class 7 maths CBSE?

A: To simplify exponents and power in class 7 maths CBSE, we need to follow the order of operations (PEMDAS) and simplify the expression step by step. We need to evaluate the exponents, simplify the expression, and then perform any remaining operations.

Q: What is the difference between exponents and power?

A: Exponents and power are used to represent repeated multiplication of a number. Exponents are the small numbers that are written above and to the right of a number, indicating how many times the base number is multiplied by itself. Power, on the other hand, is the result of raising a number to a certain power.

Q: How do we simplify expressions with exponents and power?

A: To simplify expressions with exponents and power, we need to follow the order of operations (PEMDAS) and simplify the expression step by step. We need to evaluate the exponents, simplify the expression, and then perform any remaining operations.

Q: What is the final simplified expression for 36×p⁸×6⁵/6×z³?

A: The final simplified expression for 36×p⁸×6⁵/6×z³ is p⁸×1296/z³.

Q: How do we handle negative exponents?

A: Negative exponents can be handled by taking the reciprocal of the base number. For example, a⁻¹ is equal to 1/a.

Q: What is the rule for multiplying exponents with the same base?

A: When multiplying exponents with the same base, we add the exponents. For example, a⁵×a³ = a⁸.

Q: What is the rule for dividing exponents with the same base?

A: When dividing exponents with the same base, we subtract the exponents. For example, a⁵/a³ = a².

Q: How do we handle exponents with different bases?

A: When dealing with exponents with different bases, we cannot add or subtract the exponents. Instead, we need to multiply the numbers.

Q: What is the importance of simplifying exponents and power in class 7 maths CBSE?

A: Simplifying exponents and power in class 7 maths CBSE is important because it helps us to solve complex mathematical problems more efficiently. By simplifying expressions with exponents and power, we can reduce the complexity of the problem and make it easier to solve.

Q: How can I practice simplifying exponents and power in class 7 maths CBSE?

A: You can practice simplifying exponents and power in class 7 maths CBSE by working on sample problems and exercises. You can also try to simplify expressions with exponents and power on your own, using the rules and concepts that you have learned.

Q: What are some common mistakes to avoid when simplifying exponents and power in class 7 maths CBSE?

A: Some common mistakes to avoid when simplifying exponents and power in class 7 maths CBSE include:

Not following the order of operations (PEMDAS)
Not simplifying the expression step by step
Not handling negative exponents correctly
Not using the correct rules for multiplying and dividing exponents with the same base

By avoiding these common mistakes, you can ensure that you are simplifying exponents and power correctly in class 7 maths CBSE.