Power of a Product Rule
In Power of a Product Rule, two different bases are raised to the same power are multiplied, then, bases are multiplied and power is common to the product of the bases. It is represented as (xm × ym) = (xy)m. If the given question is (xy)m then distribute the exponent to each portion of the base when multiplying any base by an exponent, hence (xy)m = (xm × ym)
Example: 23×33 =?
Solution:
Since the bases are different and the power is same then multiply the bases and raise it to the common power.
Therefore, 23×33 =(2×3)3 = 63 = 216
Example: (2×3)3 =?
Solution:
In this case separate the same power to individual bases.
Hence, (2×3)3 = 23×33 = 8×27 = 216
Laws of Exponents
Laws of Exponents: Exponents are a way of representing very large or very small numbers. Exponent rules are the laws of the exponents that are used to solve various exponents’ problems. The multiplication, division, and other operations on exponents can be achieved using these laws of exponents. There are different rules of exponents also called laws of exponents in Mathematics and all these laws are added in the article below.
In this article, we will learn about Exponents Definition, Laws of Exponents, Laws of Exponents Examples, and others in detail.
Table of Content
- Exponents Definition
- What are Exponent Rules?
- What are Laws of Exponents?
- Product of Powers Rule
- Quotient of Powers Rule
- Power of a Power Rule
- Power of a Product Rule
- Power of a Quotient Rule
- Zero Power Rule
- Negative Exponent Rule
- Fractional Exponent Rule (Laws of Exponents with Fractions)
- Other Rules of Exponents
- Laws of Exponents and Logarithms
- Table: Laws of Exponents
- Exponent Rules Examples