Exponents 4 – Product Law

Table of Contents

• Product Law of Exponents
• Problems
• Summary
• What’s Next?

In the previous segment, we learnt about Negative base exponents. We will now learn about the Laws of exponents. In this segment, we will learn about the Product law of exponents.

What is the Product law of exponents?

The Product law of exponents states that,

For any non-zero integer a, ?^? × ?^? = ?^?+?, where m and n are integers.

For example,

2² × 2³ = 2²⁺³ = 2⁵

This law applies to only the multiplication of exponential forms with the same base.

Problems based on product law

Q. Express ?^? × ?^?? in exponential form. Solution:

As the bases are the same, using the product law,

37 × 314 = 37+14 = 321.

Q. Express ?^? × ?^? × ?^? in exponential form. Solution:

As the bases are the same, using the product law,

43 × 42 × 45 = 43+2+5 = 410

Summary

Product Law of Exponents

For any non-zero integer a, ?? × ?? = ??+?,where m and n are integers.

What’s next?

In the next segment of Class 7 Maths, we will learn about the Quotient law of exponents