The Lesson
We can find a power of a product. To find a power of a product, raise each letter in the product to the exponent.This is a law of exponents.
How to Find the Power of a Product in Algebra
Finding a power of a product in algebra is easy.Question
Use the law of exponents to find the power of the product below.StepbyStep:
1
Find the exponent. In our example, the exponent is 2.
2
Find the first letter in the product. In our example, the first letter is x.
3
Raise the letter found in Step 2 (x) to the exponent found in Step 1 (2). This becomes the first part of the answer.
4
Find the second letter in the product. In our example, the second letter is y.
5
Raise the letter found in Step 4 (y) to the exponent found in Step 1 (2). This becomes the second part of the answer.
Answer:
We have found the power of the product.Understanding Powers of a Product in Algebra
 The power is (ab)^{n}.

The base is the product ab.
It is a product because it has factors (a and b) multiplied together. (See Note: What Is a Factor in Algebra?).
ab = a × b
 The exponent is n.

a^{n}b^{n} is a product of the powers a^{n} and b^{n}.
a^{n}b^{n} = a^{n} × b^{n}
More Examples of Finding the Power of a Product in Algebra
Products in algebra do not just consist of single letters multiplying each other.
When a factor is a number, we can find the power:

When a factor is a term, we can find the power. Notice that the whole term is raised to the exponent:

When a factor is an expression, we can find the power. Notice that the whole expression is raised to the exponent: