What is the Product law of exponents?

---

The Product law of exponents states that,

For any non-zero integer a, 𝑎^𝑚 × 𝑎^𝑛 = 𝑎^𝑚+𝑛, 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

• Express 𝟑^𝟕 × 𝟑^𝟏𝟒in exponential form. Solution:

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

37 × 314 = 37+14 = 321.

• Express 𝟒^𝟑 × 𝟒^𝟐 × 𝟒^𝟓in 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, 𝑎𝑚 × 𝑎𝑛 = 𝑎𝑚+𝑛,where m and n are integers.